IDA Framework

The IDA framework consists of six steps [Huebner et al 2018, Figure 1], here we assume that metadata (step I) exist in sufficient detail, and that data cleaning (step II) was already performed. Metadata summarize background information about the data to properly conduct IDA steps, and a data cleaning process identifies and corrects technical errors. The data screening (step III) examines data properties to inform decisions about the intended analysis. Initial data reporting (step IV) document insight of the previous steps and can be referred to when interpreting results from the regression modeling. Consequences of these analyses can be that the analysis plan needs to be refined or updated (step V). Finally, reporting of IDA results in research papers (step VI) are necessary to ensure transparency regarding key findings that influence the analysis or interpretation of results. Further details about the elements of IDA are discussed in [TG3 papers].

IDA framework

References

Huebner M, le Cessie S, Schmidt CO, Vach W . A contemporary conceptual framework for initial data analysis. Observational Studies 2018; 4: 171-192. Link

Huebner M, Vach W, le Cessie S, Schmidt C, Lusa L. Hidden Analyses: a review of reporting practice and recommendations for more transparent reporting of initial data analyses. BMC Med Res Meth 2020; 20:61. Link

Scope of the regression analyses for the examples

Regression models can be used for a wide range of purposes, for the purpose of these examples the assumptions on the regression analysis set-up in this paper are listed in Table 1. Thus, IDA tasks will be explained in a well-defined, practically relevant setting. Since a key principle is that IDA does not touch the research question no associations between dependent (outcome) and independent (non-outcome) variables are considered.

Table 1: The scope of the regression analyses considered for IDA tasks

Aspects of the research plan	Assumptions in this paper	Reason for the assumption
Dependent (outcome) variable	One dependent variable that can be continuous or binary; exclude time-to-event or longitudinal outcomes	Explain IDA tasks in a well-defined, practically relevant setting
Regression models	Models with linear predictors	Explain IDA tasks in a well-defined, practically relevant setting
Purpose of regression model	Adjust effect of one variable of interest for confounders; quantify the effects of explanatory variables on the outcome	Explain IDA tasks in a well-defined, practically relevant setting
Independent variables	“explanatory” or “confounder” depending on purpose of model; small to moderate number of mixed types; Not high dimensional; no repeated measurements	To demonstrate IDA approaches for a mix of variables likely to be encountered in practice
Statistical analysis plan	Exists, defines the outcome variable, the type of regression model to be used, and a set of independent variables	IDA does not touch the research question, but may lead to an update or refinement of the analysis plan

References:

Vach W. Regression Models as a Tool in Medical Research. Chapman/Hall CRC 2012

Harrell FE. Regression Modeling Strategies. Springer (2nd ed) 2015

Royston P and Sauerbrei W. Multivariable Model Building. Wiley (2008)

[…]

Data screening and possible actions

Univariate distributions

	What to look at	Possible actions: Interpretation	Possible actions: SAP	Possible actions: Presentation
Continuous variables	General skewness	Help in interpreting results	Update SAP	Update intended presentation of results
Continuous variables	General skewness	Wide CI for coefficients	Use variable as log-transformed	Update intended presentation of results
Continuous variables	Outliers	Disproportional impact on results	Winsorize or transform	Model involves winsorization
Continuous variables	Spike at 0	Narrow CI at 0	Use appropriate representation of variable in model	Use 2 (or more) coefficients to distinguish 0 from non-0 continuous part
Categorical variables	Frequencies	Comparisons to default reference probably irrelevant	Change reference category	Contrasts compare to (new) reference category
Categorical variables	Rare categories	Wide CI for coefficients	Collapse/exclude	Fewer categories to present
Categorical variables	One very frequent category	Comparisons irrelevant?	Exclude variable	Variable omitted

Bivariate distributions

	What to look at	Possible actions: Interpretation	Possible actions: SAP	Possible actions: Presentation
Continuous by continuous	Outliers (from the cloud)	Disproportional impact on results	Winsorize or transform	Model involves winsorization
Continuous by continuous	Correlations	Wide CI for coefficients	Winsorize or transform	Model involves winsorization
Continuous by categorical	Outliers (only visible in bivariate plot)	Wide CI for coefficients
Categorical by categorical	Frequent/rare combinations	Comparison to default reference irrelevant	Change reference category	Contrasts compare to (new) reference category
Categorical by categorical	Frequent/rare combinations	interactions relevant?	Remove interaction from model	Fewer interactions to present

Missing values

	What to look at	Possible actions: Interpretation	Possible actions: SAP	Possible actions: Presentation
Per variable	Number and proportion	Wide CI for coefficients	Remove variable if many missing values
Pattern	Variables missing independently or together		Omit variables together	Changes model
Pattern	Variables missing dependent on levels of other variables	Systematic missingness? Model still based on representative?	IPW needed?	Weighted analysis
Complete cases	Number and proportion	Few cases left for main CCO analysis	Multiple imputation (or other way of dealing with missing values)?	Result from MI analysis? Or applicability restricted to a subpopulation?

References

Huebner M, le Cessie S, Schmidt CO, Vach W . A contemporary conceptual framework for initial data analysis. Observational Studies 2018; 4: 171-192. Link

Harrell FE. Regression Modeling Strategies. Springer (2nd ed) 2015

[…]

CRASH-2

Introduction to CRASH-2

Since a key principle of IDA is not to touch the research questions, before IDA commences the research aim and statistical analysis plan need to be in place. IDA may lead to an update or refinement of the analysis plan. To demonstrate the workflow and content of IDA, we created a hypothetical research aim and corresponding statistical analysis plan, which is described in more detail in the section Crash2_SAP.Rmd.

Hypothetical research aim for IDA is to develop a multivariable model for early death (death within 28 days from injury) using nine independent variables of mixed type (continuous, categorical, semicontinuous) with the primary aim of prediction and a secondary aim of describing the association of each variable with the outcome.

A prediction model was developed and validated based on this data set in “Predicting early death in patients with traumatic bleeding” Perel et al, BMJ 2012, [supplement available at]. The assumed research aim is in line with the prediction model

CRASH-2 Description

Clinical Randomisation of an Antifibrinolyticin Significant Haemorrhage(CRASH-2) was a large randomised placebo controlled trial among trauma patients with, or at risk of, significant haemorrhage, of the effects of antifibrinolytic treatment on death and transfusion requirement. The study is described at the original trial website. A public version of the data set is found at a repository of public data sets hosted by the Vanderbilt University’s Department of Biostatistics (Prof. Frank Harrell Jr.).

The data set includes 20,207 patients and 44 variables.

Note: In contrast to the analysis described in Perel et al, variables describing the economic region and the treatment allocation are missing in the public version of the data set, and while the data set contains 20,207 patients, the research paper mentions 20,127 patients having been included in the study.

Crash2 dataset contents

Source dataset

We refer to the source data set as the dataset available online here

Display the source dataset contents. This dataset is in the data-raw folder of the project directory.

Data frame:crash2

20207 observations and 44 variables, maximum # NAs:17121

Name	Labels	Units	Levels	Class	Storage	NAs
entryid	Unique Numbers for Entry Forms			integer	integer	0
source	Method of Transmission of Entry Form to CC		5		integer	0
trandomised	Date of Randomization			Date	double	0
outcomeid	Unique Number From Outcome Database			integer	integer	80
sex			2		integer	1
age					integer	4
injurytime	Hours Since Injury			numeric	double	11
injurytype			3		integer	0
sbp	Systolic Blood Pressure	mmHg		integer	integer	320
rr	Respiratory Rate	/min		integer	integer	191
cc	Central Capillary Refille Time	s		integer	integer	611
hr	Heart Rate	/min		integer	integer	137
gcseye	Glasgow Coma Score Eye Opening			integer	integer	732
gcsmotor	Glasgow Coma Score Motor Response			integer	integer	732
gcsverbal	Glasgow Coma Score Verbal Response			integer	integer	735
gcs	Glasgow Coma Score Total			integer	integer	23
ddeath	Date of Death			Date	double	17121
cause	Main Cause of Death		7		integer	17118
scauseother	Description of Other Cause of Death		227		integer	0
status	Status of Patient at Outcome if Alive		3		integer	3169
ddischarge	Date of discharge, transfer to other hospital or day 28 from randomization			Date	double	3185
condition	Condition of Patient at Outcome if Alive		5		integer	3251
ndaysicu	Number of Days Spent in ICU			numeric	double	182
bheadinj	Significant Head Injury			integer	integer	80
bneuro	Neurosurgery Done			integer	integer	80
bchest	Chest Surgery Done			integer	integer	80
babdomen	Abdominal Surgery Done			integer	integer	80
bpelvis	Pelvis Surgery Done			integer	integer	80
bpe	Pulmonary Embolism			integer	integer	80
bdvt	Deep Vein Thrombosis			integer	integer	80
bstroke	Stroke			integer	integer	80
bbleed	Surgery for Bleeding			integer	integer	80
bmi	Myocardial Infarction			integer	integer	80
bgi	Gastrointestinal Bleeding			integer	integer	80
bloading	Complete Loading Dose of Trial Drug Given			integer	integer	80
bmaint	Complete Maintenance Dose of Trial Drug Given			integer	integer	80
btransf	Blood Products Transfusion			integer	integer	80
ncell	Number of Units of Red Call Products Transfused			numeric	double	9963
nplasma	Number of Units of Fresh Frozen Plasma Transfused			integer	integer	9964
nplatelets	Number of Units of Platelets Transfused			integer	integer	9964
ncryo	Number of Units of Cryoprecipitate Transfused			integer	integer	9964
bvii	Recombinant Factor VIIa Given			integer	integer	374
boxid	Treatment Box Number			integer	integer	0
packnum	Treatment Pack Number			integer	integer	0

Variable	Levels
source	telephone
	telephone entered manually
	electronic CRF by email
	paper CRF enteredd in electronic CRF
	electronic CRF
sex	male
	female
injurytype	blunt
	penetrating
	blunt and penetrating
cause	bleeding
	head injury
	myocardial infarction
	stroke
	pulmonary embolism
	multi organ failure
	other
scauseother
	Acute Hypoxia
	ACUTE LUNG INJURY
	Acute Pulmonary Oedema
	Acute Renal Failure
	ACUTE RESPIRATORY DISTRESS SYNDROME (ARDS)
	acute respiratory failure
	acute respiratory failure+sepsis
	air amboli (embolism)
	Air embolism caused by penetrating lung trauma
	...
status	discharged
	still in hospital
	transferred to other hospital
condition	no symptoms
	minor symptoms
	some restriction in lifestyle but independent
	dependent, but not requiring constant attention
	fully dependent, requiring attention day and night

Updated analysis dataset

Additional meta-data is added to the original source data set. We write this new modified data set back to the data folder after adding additional meta-data for the following variables:

age - add label “Age” and unit “years”.
injury time - add unit “hours”.
total Glasgow coma score - add unit “points”.

At the stage we select the variables of interest to take in to the IDA phase by dropping variables we do not check in IDA.

As a cross check we display the contents again to ensure the additional data is added, and then write back the changes to the data folder in the file “data/a_crash2.rds”.

Input object size: 1221480 bytes; 12 variables 20207 observations New object size: 1223272 bytes; 12 variables 20207 observations Input object size: 1546808 bytes; 14 variables 20207 observations New object size: 1385720 bytes; 14 variables 20207 observations

Data frame:a_crash2

20207 observations and 14 variables, maximum # NAs:17121

Name	Labels	Units	Levels	Class	Storage	NAs
entryid	Unique Numbers for Entry Forms			integer	integer	0
trandomised	Date of Randomization			Date	double	0
ddeath	Date of Death			Date	double	17121
age	Age	years		integer	integer	4
sex	Sex		2		integer	1
sbp	Systolic Blood Pressure	mmHg		integer	integer	320
hr	Heart Rate	/min		integer	integer	137
rr	Respiratory Rate	/min		integer	integer	191
gcs	Glasgow Coma Score Total	points		integer	integer	23
cc	Central Capillary Refille Time	s		integer	integer	611
injurytime	Hours Since Injury	hours		numeric	double	11
injurytype	Injury type		3		integer	0
time2death					integer	17121
earlydeath	Death within 28 days from injury			integer	integer	0

Variable	Levels
sex	male
	female
injurytype	blunt
	penetrating
	blunt and penetrating

Section session info

## R version 4.0.2 (2020-06-22)
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## [1] stats     graphics  grDevices utils     datasets  methods   base     
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##  [9] readr_1.4.0     tidyr_1.1.2     tibble_3.0.6    ggplot2_3.3.3  
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## [61] jpeg_0.1-8.1        yaml_2.2.1          colorspace_2.0-0   
## [64] cluster_2.1.0       rvest_0.3.6         knitr_1.31         
## [67] haven_2.3.1

Statistical analysis plan

Since a key principle of IDA is not to touch the research questions, before IDA commences the research aim and statistical analysis plan needs to be in place. IDA may lead to an update or refinement of the analysis plan. To demonstrate the workflow and content of IDA, we created a hypothetical research aim and corresponding statistical analysis plan.

Hypothetical research aim for IDA: Develop a multivariable model for early death (death within 28 days from injury) using nine independent variables of mixed type (continuous, categorical, semicontinuous) with the primary aim of prediction and a secondary aim of describing the association of each variable with the outcome.

The assumed analysis aim is in line with the prediction model presented by Perel et al, BMJ 2012, supplement available at.

Outcome variable

Early death, i.e. in-hospital death within 28 days from injury (binary variable)

Statistical methods

Logistic regression will be used to model early death by the following independent variables (measured at randomisation) deemed important to predict early death.

Demographic measurements:

Age (age, years)
Sex (sex, male or female)

Physiological measurements:

Systolic blood pressure (sbp, mmHg)
Heart rate (hr, 1/min)
Respiratory rate (rr, 1/min)
Glasgow coma score (gcs, points)
Central capillary refill time (cc, seconds)

Characteristics of injury measurements:

Time since injury (injurytime, hours)
Type of injury (injurytype, ‘blunt’, ‘penetrating’ or ‘blunt and penetrating’)

Restricted cubic splines with 3 degrees of freedom with knots set to default values will be used for continuous variables. As the final prediction model should be parsimonious enough to simplify its application, a backward elimination algorithm with a significance level set at \(\alpha=0.05\) will be applied to remove statistically insignificant effects. Finally, nonlinear representation of each continuous variable will be tested against linear representation at \(\alpha=0.05\). In case of lacking added value of a nonlinear effect, the model will be refitted with a linear effect for that variable.

Remarks

Regarding type of injury, the original paper describes its treatment in the model as follows: ‘Type of injury had three categories—-penetrating, blunt, or blunt and penetrating—but we analysed it as ’penetrating’ or ‘blunt and penetrating.’ ’ It is not clear from that description what happened to the ‘blunt’ group. (I assume they were collapsed with ‘blunt and penetrating’.) ** we are going to consider the three categories, and then check aout recommendations for the final analysis-MH**
The original paper describes the modeling approach as follows: ‘We used a backward step-wise approach. Firstly, we included all potential prognostic factors and interaction terms that users considered plausible. These interactions included all potential predictors with type of injury, time since injury, and age. We then removed, one at a time, terms for which we found no strong evidence of an association, judged according to the P values (<0.05) from the Wald test.’ This would mean they tested at least 24 interaction terms, each possibly using several degrees of freedom! In the final model, only an interaction of Glasgow coma score and type of injury was included.

Preparations

The outcome variable, early death (i.e., death within 28 days from injury) must be computed from the time span between date of death and date of randomization using the following logic:

transform ddeath and trandomisation into an interpretable date format and then compute the difference
interpret missing (i.e. NAs) as ‘not died within study period, at least not within 28 days’
if patients died after 28 days, treat as alive

This can be derived using the following code logic:

## NOTE: This is for demostration purposes, this code is not run here. 
## The derivation was executed earlier. 

a_crash2$time2death <-
  as.numeric(as.Date(a_crash2$ddeath) - as.Date(a_crash2$trandomised))

a_crash2$earlydeath[!is.na(a_crash2$time2death)] <-
  (a_crash2$time2death[!is.na(a_crash2$time2death)] <= 28) + 0

# +0 to transform it from TRUE/FALSE to 1/0
# NA in time2death means alive at day 28
a_crash2$earlydeath[is.na(a_crash2$time2death)] <- 0

We also display the marginal distribution of the derived outcome variable.

a_crash2 %>%
  dplyr::select(earlydeath) %>%
  gtsummary::tbl_summary()

Characteristic	N = 20,207¹
Death within 28 days from injury	3,076 (15%)
¹ n (%)

The number of deaths computed in the data set coincides with the number reported in Perel et al, BMJ 2012.

Sources

Data obtained from http://biostat.mc.vanderbilt.edu/wiki/Main/DataSets

To download the data set, click the link to data set

Data dictionary

The data dictionary can be found LINK

References

CRASH-2 Collaborators. Effects of tranexamic acid on death, vascular occlusive events, and blood transfusion in trauma patients with significant haemorrhage (CRASH-2): a randomised, placebo-controlled trial. Lancet 2010;376:23-32

Perel P, Prieto-Merino D, Shakur H, Clayton T, Lecky F, Bouamra O, Russell R, Faulkner M, Steyerberg EW, Roberts I. Predicting early death in patients with traumatic bleeding: development and validation of prognostic model. BMJ 2012; 345(aug15 1): e5166.

Missing data

Per variable missingness

Number and percentage of missing.

Variable	Missing (count)	Missing (%)
cc	611	3.02
sbp	320	1.58
rr	191	0.95
hr	137	0.68
gcs	23	0.11
injurytime	11	0.05
age	4	0.02
sex	1	0.00
injurytype	0	0.00

Missingness patterns over variables

(In)complete cases

This section presents patients with a least one missing value. First we list out patients with at least one missing value in a filterable table.

Then we report the pattern of missing for this set of patients.

Section session info

## R version 4.0.2 (2020-06-22)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 18363)
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## [2] LC_CTYPE=English_United States.1252   
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C                          
## [5] LC_TIME=English_United States.1252    
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] DT_0.17          kableExtra_1.3.1 gt_0.2.2         naniar_0.6.0    
##  [5] Hmisc_4.5-0      Formula_1.2-4    survival_3.1-12  lattice_0.20-41 
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## [13] readr_1.4.0      tidyr_1.1.2      tibble_3.0.6     ggplot2_3.3.3   
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Univariate distribution checks

This section reports a series of univariate summary checks of the CRASH-2 dataset.

Data set overview

Using the Hmisc describe function, we provide an overview of the data set. The descriptive report also provides histograms of continuous variables. For ease of scanning the information, we group the report by measurement type.

Demographic variables

Demographic variables

2 Variables 20207 Observations

age: Age years

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
20203	4	84	0.999	34.56	15.55	18	19	24	30	43	55	64

lowest : 1 14 15 16 17 , highest: 92 94 95 96 99

sex: Sex

n	missing	distinct
20206	1	2

 Value        male female
 Frequency   16935   3271
 Proportion  0.838  0.162

Physiological measurements

Physiological measurements

5 Variables 20207 Observations

sbp: Systolic Blood Pressure mmHg

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
19887	320	173	0.989	98.45	27.86	60	70	80	95	110	130	143

lowest : 4 10 12 20 25 , highest: 225 230 234 240 250

hr: Heart Rate /min

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
20070	137	173	0.996	104.5	23.38	70	80	90	105	120	130	140

lowest : 3 4 5 6 10 , highest: 190 192 198 200 220

rr: Respiratory Rate /min

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
20016	191	68	0.99	23.06	7.052	14	16	20	22	26	30	35

lowest : 1 2 3 4 5 , highest: 90 91 94 95 96

gcs: Glasgow Coma Score Total points

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
20184	23	13	0.863	12.47	3.594	4	6	11	15	15	15	15

lowest : 3 4 5 6 7 , highest: 11 12 13 14 15

 Value          3     4     5     6     7     8     9    10    11    12    13    14
 Frequency    784   520   441   584   733   576   504   663   586   951  1356  2140
 Proportion 0.039 0.026 0.022 0.029 0.036 0.029 0.025 0.033 0.029 0.047 0.067 0.106
                 
 Value         15
 Frequency  10346
 Proportion 0.513

cc: Central Capillary Refille Time s

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
19596	611	20	0.945	3.267	1.67	1	2	2	3	4	5	6

lowest : 1 2 3 4 5 , highest: 17 18 20 30 60

 Value          1     2     3     4     5     6     7     8     9    10    11    12
 Frequency   1510  5328  6020  3367  1805   802   268   271    45   139     3     7
 Proportion 0.077 0.272 0.307 0.172 0.092 0.041 0.014 0.014 0.002 0.007 0.000 0.000
                                                           
 Value         13    15    16    17    18    20    30    60
 Frequency      3    19     3     1     1     2     1     1
 Proportion 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000

Characteristics of injury

Characteristics of injury

2 Variables 20207 Observations

injurytime: Hours Since Injury hours

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
20196	11	93	0.972	2.844	2.35	0.5	1.0	1.0	2.0	4.0	6.0	7.0

lowest : 0.10 0.15 0.20 0.25 0.30 , highest: 22.00 45.00 48.00 72.00 96.00

injurytype: Injury type

n	missing	distinct
20207	0	3

 Value                      blunt           penetrating blunt and penetrating
 Frequency                  11189                  6552                  2466
 Proportion                 0.554                 0.324                 0.122

Categorical variables

We now provide a closer visual examination of the categorical predictors.

Categorical ordinal plots

The Glasgow coma score, an ordinal categorical variable, is also displayed separately.

Continuous variables

A closer visual examination of continuous predictors.

There is evidence of digit preference. Explore further with targeted summaries. A more detailed univariate summaries for the variables of interest are also provided below.

Age

Distribution of subject age [years]

Five patients under the age of 17, the inclusion criteria for the study, with one patient aged 1.

Blood pressure

Distribution of SBP

Respiratory rate

Distribution of respiratory rate

Heart rate

Distribution of heart rate

Central capillary refill time

Distribution of Central capillary refill time

Hours since injury

Distribution of hours since injury

Section session info

## R version 4.0.2 (2020-06-22)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 18363)
## 
## Matrix products: default
## 
## locale:
## [1] LC_COLLATE=English_United States.1252 
## [2] LC_CTYPE=English_United States.1252   
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C                          
## [5] LC_TIME=English_United States.1252    
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] Hmisc_4.5-0     Formula_1.2-4   survival_3.1-12 lattice_0.20-41
##  [5] forcats_0.5.1   stringr_1.4.0   dplyr_1.0.4     purrr_0.3.4    
##  [9] readr_1.4.0     tidyr_1.1.2     tibble_3.0.6    ggplot2_3.3.3  
## [13] tidyverse_1.3.0 here_1.0.1     
## 
## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.6          lubridate_1.7.9.2   png_0.1-7          
##  [4] assertthat_0.2.1    rprojroot_2.0.2     digest_0.6.27      
##  [7] R6_2.5.0            cellranger_1.1.0    backports_1.2.1    
## [10] reprex_1.0.0        evaluate_0.14       highr_0.8          
## [13] httr_1.4.2          pillar_1.4.7        rlang_0.4.10       
## [16] readxl_1.3.1        data.table_1.13.6   rstudioapi_0.13    
## [19] rpart_4.1-15        Matrix_1.2-18       checkmate_2.0.0    
## [22] rmarkdown_2.6       labeling_0.4.2      splines_4.0.2      
## [25] foreign_0.8-80      htmlwidgets_1.5.3   munsell_0.5.0      
## [28] broom_0.7.4         compiler_4.0.2      modelr_0.1.8       
## [31] xfun_0.20           pkgconfig_2.0.3     base64enc_0.1-3    
## [34] htmltools_0.5.1.1   nnet_7.3-14         tidyselect_1.1.0   
## [37] htmlTable_2.1.0     gridExtra_2.3       bookdown_0.21      
## [40] crayon_1.4.1        dbplyr_2.1.0        withr_2.4.1        
## [43] grid_4.0.2          jsonlite_1.7.2      gtable_0.3.0       
## [46] lifecycle_0.2.0     DBI_1.1.1           magrittr_2.0.1     
## [49] scales_1.1.1        rmdformats_1.0.1    cli_2.3.0          
## [52] stringi_1.5.3       farver_2.0.3        fs_1.5.0           
## [55] latticeExtra_0.6-29 xml2_1.3.2          ellipsis_0.3.1     
## [58] generics_0.1.0      vctrs_0.3.6         RColorBrewer_1.1-2 
## [61] tools_4.0.2         glue_1.4.2          hms_1.0.0          
## [64] jpeg_0.1-8.1        yaml_2.2.1          colorspace_2.0-0   
## [67] cluster_2.1.0       rvest_0.3.6         knitr_1.31         
## [70] haven_2.3.1         patchwork_1.1.1

Multivariate distributions

Overview

Variable correlation

corrs <- a_crash2 %>%
  dplyr::select(age, sex, sbp, hr, rr ,cc, injurytime, injurytype ) %>%
  filter(complete.cases(.)) %>%
  dplyr::mutate_all(as.numeric)

M <- cor(corrs)
col <- colorRampPalette(c("#BB4444", "#EE9988", "#FFFFFF", "#77AADD", "#4477AA"))
corrplot(M, method = "color", col = col(200),
         type = "upper", order = "hclust", number.cex = .7,
         addCoef.col = "black", # Add coefficient of correlation
         tl.col = "black", tl.srt = 90, # Text label color and rotation
         # hide correlation coefficient on the principal diagonal
         diag = FALSE)

Variable clustering

Variable clustering is used for assessing collinearity, redundancy, and for separating variables into clusters that can be scored as a single variable, thus resulting in data reduction.

Hmisc::varclus( ~ age +  sbp +  hr + rr + cc + gcs + injurytime + injurytype + sex, data = a_crash2)

## Hmisc::varclus(x = ~age + sbp + hr + rr + cc + gcs + injurytime + 
##     injurytype + sex, data = a_crash2)
## 
## 
## Similarity matrix (Spearman rho^2)
## 
##                                  age  sbp   hr   rr   cc  gcs injurytime
## age                             1.00 0.00 0.00 0.00 0.00 0.00       0.01
## sbp                             0.00 1.00 0.11 0.03 0.07 0.01       0.01
## hr                              0.00 0.11 1.00 0.05 0.02 0.02       0.00
## rr                              0.00 0.03 0.05 1.00 0.02 0.00       0.00
## cc                              0.00 0.07 0.02 0.02 1.00 0.02       0.00
## gcs                             0.00 0.01 0.02 0.00 0.02 1.00       0.01
## injurytime                      0.01 0.01 0.00 0.00 0.00 0.01       1.00
## injurytypepenetrating           0.02 0.00 0.01 0.00 0.00 0.06       0.05
## injurytypeblunt and penetrating 0.00 0.01 0.01 0.00 0.00 0.01       0.00
## sexfemale                       0.01 0.00 0.00 0.00 0.00 0.00       0.00
##                                 injurytypepenetrating
## age                                              0.02
## sbp                                              0.00
## hr                                               0.01
## rr                                               0.00
## cc                                               0.00
## gcs                                              0.06
## injurytime                                       0.05
## injurytypepenetrating                            1.00
## injurytypeblunt and penetrating                  0.07
## sexfemale                                        0.02
##                                 injurytypeblunt and penetrating sexfemale
## age                                                        0.00      0.01
## sbp                                                        0.01      0.00
## hr                                                         0.01      0.00
## rr                                                         0.00      0.00
## cc                                                         0.00      0.00
## gcs                                                        0.01      0.00
## injurytime                                                 0.00      0.00
## injurytypepenetrating                                      0.07      0.02
## injurytypeblunt and penetrating                            1.00      0.00
## sexfemale                                                  0.00      1.00
## 
## No. of observations used for each pair:
## 
##                                   age   sbp    hr    rr    cc   gcs injurytime
## age                             20203 19884 20066 20012 19593 20180      20193
## sbp                             19884 19887 19795 19750 19316 19883      19877
## hr                              20066 19795 20070 19943 19482 20066      20059
## rr                              20012 19750 19943 20016 19454 20014      20008
## cc                              19593 19316 19482 19454 19596 19595      19588
## gcs                             20180 19883 20066 20014 19595 20184      20173
## injurytime                      20193 19877 20059 20008 19588 20173      20196
## injurytypepenetrating           20203 19887 20070 20016 19596 20184      20196
## injurytypeblunt and penetrating 20203 19887 20070 20016 19596 20184      20196
## sexfemale                       20202 19886 20069 20015 19595 20183      20195
##                                 injurytypepenetrating
## age                                             20203
## sbp                                             19887
## hr                                              20070
## rr                                              20016
## cc                                              19596
## gcs                                             20184
## injurytime                                      20196
## injurytypepenetrating                           20207
## injurytypeblunt and penetrating                 20207
## sexfemale                                       20206
##                                 injurytypeblunt and penetrating sexfemale
## age                                                       20203     20202
## sbp                                                       19887     19886
## hr                                                        20070     20069
## rr                                                        20016     20015
## cc                                                        19596     19595
## gcs                                                       20184     20183
## injurytime                                                20196     20195
## injurytypepenetrating                                     20207     20206
## injurytypeblunt and penetrating                           20207     20206
## sexfemale                                                 20206     20206
## 
## hclust results (method=complete)
## 
## 
## Call:
## hclust(d = as.dist(1 - x), method = method)
## 
## Cluster method   : complete 
## Number of objects: 10

Plot associations.

plot(Hmisc::varclus( ~ age +  sbp +  hr + rr + cc + gcs + injurytime + injurytype + sex, data = a_crash2))

Variable redundancy

Redundancy analysis of predictor variables.

Hmisc::redun( ~ hr + rr + age + sbp + injurytype + sex  , data = a_crash2)

## 
## Redundancy Analysis
## 
## Hmisc::redun(formula = ~hr + rr + age + sbp + injurytype + sex, 
##     data = a_crash2)
## 
## n: 19689     p: 6    nk: 3 
## 
## Number of NAs:    518 
## Frequencies of Missing Values Due to Each Variable
##         hr         rr        age        sbp injurytype        sex 
##        137        191          4        320          0          1 
## 
## 
## Transformation of target variables forced to be linear
## 
## R-squared cutoff: 0.9    Type: ordinary 
## 
## R^2 with which each variable can be predicted from all other variables:
## 
##         hr         rr        age        sbp injurytype        sex 
##      0.116      0.044      0.052      0.099      0.061      0.035 
## 
## No redundant variables

Summary reports by sex

Overall

	N	male N=16935	female N=3271
Baseline characteristics by sex.
Age years	20203	23.0 30.0 41.0 33.7 ± 13.6	25.0 35.0 50.0 38.8 ± 16.8
Systolic Blood Pressure mmHg	19887	80.0 95.0 110.0 98.8 ± 25.5	80.0 90.0 110.0 96.7 ± 25.7
Heart Rate /min	20070	90.0 105.0 120.0 104.3 ± 21.2	92.0 106.0 120.0 105.2 ± 21.0
Respiratory Rate /min	20016	20.00 22.00 26.00 23.07 ± 6.77	20.00 22.00 26.00 23.03 ± 6.58
Central Capillary Refille Time s	19596	2.00 3.00 4.00 3.27 ± 1.72	2.00 3.00 4.00 3.23 ± 1.59
Glasgow Coma Score Total points	20184	11.00 15.00 15.00 12.44 ± 3.72	12.00 14.00 15.00 12.62 ± 3.46
Hours Since Injury hours	20196	1.00 2.00 4.00 2.85 ± 2.39	1.00 2.00 4.00 2.84 ± 2.67
Injury type : blunt	20207	0.53 ⁸⁹⁶²/₁₆₉₃₅	0.68 ²²²⁷/₃₂₇₁
penetrating		0.35 ⁵⁹³⁰/₁₆₉₃₅	0.19 ⁶²¹/₃₂₇₁
blunt and penetrating		0.12 ²⁰⁴³/₁₆₉₃₅	0.13 ⁴²³/₃₂₇₁
a b c represent the lower quartile a, the median b, and the upper quartile c for continuous variables. x ± s represents X ± 1 SD. N is the number of non-missing values.

Distribution of age by sex

Distribution of systolic blood pressure by sex

Distribution of heart rate by sex

Distribution of respiratory rate by sex

Distribution of central capillary refille time by sex

Distribution of central capillary refill time by sex

Distribution of hours since injury by sex

Distribution of Glasgow coma score by sex

Distribution of Glasgow coma score (point scale) by sex

Distribution of injury type by sex

Summary reports by age

Categorize age for the purposes of exploring the relationship between age and other baseline variables. This is purely for exploratory purposes only, and not to influence the analysis strategy by pursuing the dichotomization of age.

Characteristic	N = 20,207¹
age_C
<30	9,070 (45%)
30-44	6,477 (32%)
45-59	3,204 (16%)
60+	1,452 (7.2%)
NA	4 (<0.1%)
¹ n (%)

Report all variables by age category.

	N	<30 N=9070	30-44 N=6477	45-59 N=3204	60+ N=1452
Baseline characteristics by age categories.
Sex : female	20202	0.13 ¹¹⁸³/₉₀₇₀	0.15 ⁹⁵⁹/₆₄₇₆	0.21 ⁶⁵⁹/₃₂₀₄	0.32 ⁴⁶⁹/₁₄₅₂
Systolic Blood Pressure mmHg	19884	80.0 96.0 110.0 98.1 ± 23.8	80.0 90.0 110.0 97.7 ± 25.3	80.0 94.0 112.0 100.1 ± 28.4	80.0 90.0 110.0 100.4 ± 30.2
Heart Rate /min	20066	91.0 106.0 120.0 105.3 ± 21.3	90.0 106.0 120.0 104.7 ± 20.9	90.0 104.0 120.0 103.3 ± 21.0	88.0 100.0 116.0 101.0 ± 21.8
Respiratory Rate /min	20012	20.00 22.00 26.00 22.93 ± 6.74	20.00 22.00 26.00 23.24 ± 6.68	20.00 22.00 26.00 23.11 ± 6.80	20.00 22.00 26.00 23.04 ± 6.89
Central Capillary Refille Time s	19593	2.00 3.00 4.00 3.20 ± 1.77	2.00 3.00 4.00 3.27 ± 1.65	2.00 3.00 4.00 3.34 ± 1.64	2.00 3.00 4.00 3.48 ± 1.56
Glasgow Coma Score Total points	20180	11.00 15.00 15.00 12.64 ± 3.61	11.00 14.50 15.00 12.39 ± 3.72	11.00 14.00 15.00 12.38 ± 3.70	10.00 14.00 15.00 12.00 ± 3.82
Hours Since Injury hours	20193	1.00 2.00 4.00 2.71 ± 2.18	1.00 2.00 4.00 2.83 ± 2.28	1.00 2.50 4.50 3.12 ± 3.17	1.00 3.00 4.50 3.12 ± 2.68
Injury type : blunt	20203	0.50 ⁴⁵⁴⁴/₉₀₇₀	0.53 ³⁴⁶²/₆₄₇₇	0.65 ²⁰⁸¹/₃₂₀₄	0.76 ¹¹⁰¹/₁₄₅₂
penetrating		0.38 ³⁴⁴⁸/₉₀₇₀	0.33 ²¹⁵⁵/₆₄₇₇	0.23 ⁷⁴⁸/₃₂₀₄	0.14 ¹⁹⁹/₁₄₅₂
blunt and penetrating		0.12 ¹⁰⁷⁸/₉₀₇₀	0.13 ⁸⁶⁰/₆₄₇₇	0.12 ³⁷⁵/₃₂₀₄	0.10 ¹⁵²/₁₄₅₂
a b c represent the lower quartile a, the median b, and the upper quartile c for continuous variables. x ± s represents X ± 1 SD. N is the number of non-missing values.

Distribution of systolic blood pressure by age categories

Distribution of systolic blood pressure by gcs

Distribution of heart rate by age categories

Distribution of heart rate by gcs

Distribution of respiratory rate by age categories

Distribution of respiratory rate by gcs

Distribution of central capillary refille time by age categories

Distribution of central capillary refill time by gcs

WIP: multivariate scatter plots

a_crash2 %>% dplyr::filter(!is.na(sbp)) %>% tally()

##       n
## 1 19887

a_crash2 %>% dplyr::filter(is.na(sbp)) %>% tally()

##     n
## 1 320

bigN <- a_crash2 %>% dplyr::filter(!is.na(sbp) & !is.na(age)) %>% tally()
n_miss <- a_crash2 %>% dplyr::filter(is.na(sbp) | is.na(age)) %>% tally()

title <-
  paste0("Plot of ", Hmisc::label(a_crash2$age), " and ", Hmisc::label(a_crash2$sbp))

caption <-
  paste0(
    "n = ",
    bigN,
    " subjects displayed.\n",
    n_miss,
    " subjects with a missing value in at least one of the variables."
  )


x_axis <- paste0(Hmisc::label(a_crash2$age), " [", Hmisc::units(a_crash2$age), "]")
y_axis <- paste0(Hmisc::label(a_crash2$sbp), " [", Hmisc::units(a_crash2$sbp), "]")


p1 <- a_crash2 %>%
  dplyr::filter(!is.na(sbp) & !is.na(age)) %>%
  mutate(sbp = as.numeric(sbp), 
         age = as.numeric(age)) %>%
  ggplot(aes(x = sbp, y = age)) +
  ylab(x_axis) +
  xlab(y_axis) +
  labs(
    title = title,
    caption = caption
  ) +
  geom_point(shape = 16, #size = 0.5,
             alpha = 0.5,
             color = "firebrick2") +
  geom_rug() +
  theme_minimal()

p1

WIP: Scatter plots with a third or fourth variable

Scatter plot of age and RR by sex and injury type.

Scatter plot of SBP and RR by sex and injury type.

Summary reports by Glasgow coma score

	N	3 N=784	4 N=520	5 N=441	6 N=584	7 N=733	8 N=576	9 N=504	10 N=663	11 N=586	12 N=951	13 N=1356	14 N=2140	15 N=10346
Baseline characteristics by Glasgow coma score.
Age years	20203	24.0 32.0 44.0 35.5 ± 14.9	25.0 33.0 44.0 35.5 ± 14.1	24.0 32.0 45.0 35.4 ± 14.7	23.0 31.0 45.0 35.4 ± 15.4	23.0 30.0 42.0 33.9 ± 14.0	24.0 32.0 45.0 35.7 ± 15.0	24.0 32.0 44.0 35.5 ± 14.6	24.0 31.0 42.0 34.4 ± 13.8	24.0 33.0 46.0 36.6 ± 15.6	25.0 32.0 45.0 35.9 ± 14.3	25.0 33.0 45.0 36.4 ± 15.0	24.0 31.0 44.0 35.1 ± 14.7	23.0 30.0 41.0 33.7 ± 13.8
Heart Rate /min	20070	90.0 112.0 128.0 106.9 ± 31.3	95.0 114.0 130.0 110.8 ± 29.2	98.0 110.5 130.0 111.4 ± 25.4	90.0 110.0 123.2 106.2 ± 24.4	95.0 109.0 120.0 107.1 ± 23.0	95.0 110.0 120.0 107.4 ± 24.0	92.0 109.0 120.0 105.5 ± 21.9	96.0 110.0 124.8 108.4 ± 24.0	96.0 110.0 122.0 107.8 ± 20.4	100.0 110.0 122.0 109.3 ± 20.2	96.0 108.0 120.0 106.5 ± 20.1	92.0 105.0 120.0 104.5 ± 19.9	90.0 100.0 115.0 102.0 ± 18.9
Respiratory Rate /min	20016	12.00 20.00 28.00 20.67 ± 10.74	16.00 22.00 28.00 22.22 ± 9.14	18.00 22.00 28.00 22.89 ± 8.69	18.00 21.00 26.00 22.12 ± 7.56	18.00 20.00 26.00 21.97 ± 7.69	18.00 22.00 28.00 23.11 ± 7.73	20.00 24.00 28.00 23.23 ± 6.99	19.00 22.00 28.00 23.05 ± 6.73	20.00 23.00 28.00 23.45 ± 6.37	20.00 24.00 28.00 24.32 ± 6.41	20.00 22.00 27.00 23.45 ± 6.53	20.00 22.00 26.00 23.41 ± 6.09	20.00 22.00 26.00 23.14 ± 6.07
Systolic Blood Pressure mmHg	19887	70.0 85.0 103.0 88.7 ± 33.7	78.0 90.0 116.0 96.5 ± 31.2	80.0 90.0 118.0 99.0 ± 30.7	80.0 100.0 127.0 104.3 ± 32.1	80.0 100.0 130.0 105.4 ± 30.6	80.0 90.0 115.0 99.2 ± 29.4	80.0 96.0 120.0 99.6 ± 28.9	80.0 90.0 110.0 92.6 ± 28.0	80.0 90.0 110.0 94.4 ± 26.4	71.0 90.0 100.0 88.4 ± 24.7	80.0 90.0 110.0 95.9 ± 23.5	80.0 90.0 110.0 96.4 ± 22.8	90.0 100.0 110.0 100.5 ± 23.1
Central Capillary Refille Time s	19596	3.00 4.00 5.00 4.15 ± 2.13	3.00 4.00 5.00 3.84 ± 1.90	2.00 3.00 5.00 3.76 ± 1.91	2.00 3.00 4.00 3.49 ± 1.64	2.00 3.00 4.00 3.28 ± 1.55	2.00 3.00 4.00 3.52 ± 1.69	2.00 3.00 4.00 3.40 ± 3.00	2.00 3.00 4.00 3.37 ± 1.66	2.00 3.00 4.00 3.27 ± 1.51	3.00 3.00 4.00 3.53 ± 1.60	2.00 3.00 4.00 3.40 ± 1.69	2.00 3.00 4.00 3.31 ± 1.73	2.00 3.00 4.00 3.06 ± 1.54
Sex : female	20206	0.14 ¹⁰⁷/₇₈₄	0.13 ⁶⁸/₅₂₀	0.12 ⁵³/₄₄₁	0.16 ⁹²/₅₈₄	0.14 ¹⁰⁰/₇₃₃	0.15 ⁸⁹/₅₇₆	0.15 ⁷⁴/₅₀₄	0.19 ¹²⁴/₆₆₃	0.17 ⁹⁷/₅₈₆	0.21 ¹⁹⁸/₉₅₁	0.20 ²⁷⁰/₁₃₅₆	0.18 ³⁹¹/₂₁₃₉	0.16 ¹⁶⁰⁴/₁₀₃₄₆
Hours Since Injury hours	20196	1.00 2.00 4.00 2.54 ± 1.94	1.00 3.00 5.00 3.26 ± 2.20	1.00 3.00 5.00 3.42 ± 2.19	2.00 3.75 6.00 3.75 ± 2.31	2.00 3.00 5.00 3.62 ± 2.20	1.00 3.00 5.00 3.30 ± 2.17	1.00 3.00 5.00 3.12 ± 2.20	1.00 2.00 4.00 3.03 ± 2.19	1.00 2.50 4.00 3.01 ± 2.05	1.00 2.00 4.00 2.75 ± 2.03	1.00 2.00 4.00 2.79 ± 1.97	1.00 2.00 4.00 2.64 ± 1.99	1.00 2.00 4.00 2.71 ± 2.69
Injury type : blunt	20207	0.62 ⁴⁸³/₇₈₄	0.71 ³⁷¹/₅₂₀	0.73 ³²⁴/₄₄₁	0.76 ⁴⁴³/₅₈₄	0.76 ⁵⁵⁹/₇₃₃	0.69 ³⁹⁹/₅₇₆	0.67 ³³⁸/₅₀₄	0.61 ⁴⁰⁷/₆₆₃	0.64 ³⁷⁷/₅₈₆	0.58 ⁵⁵⁰/₉₅₁	0.60 ⁸¹⁴/₁₃₅₆	0.58 ¹²³⁷/₂₁₄₀	0.47 ⁴⁸⁸⁰/₁₀₃₄₆
penetrating		0.22 ¹⁷⁵/₇₈₄	0.10 ⁵³/₅₂₀	0.09 ⁴¹/₄₄₁	0.10 ⁵⁹/₅₈₄	0.11 ⁷⁷/₇₃₃	0.15 ⁸⁹/₅₇₆	0.17 ⁸⁸/₅₀₄	0.23 ¹⁵¹/₆₆₃	0.21 ¹²³/₅₈₆	0.29 ²⁷²/₉₅₁	0.24 ³²⁶/₁₃₅₆	0.29 ⁶²⁹/₂₁₄₀	0.43 ⁴⁴⁵⁸/₁₀₃₄₆
blunt and penetrating		0.16 ¹²⁶/₇₈₄	0.18 ⁹⁶/₅₂₀	0.17 ⁷⁶/₄₄₁	0.14 ⁸²/₅₈₄	0.13 ⁹⁷/₇₃₃	0.15 ⁸⁸/₅₇₆	0.15 ⁷⁸/₅₀₄	0.16 ¹⁰⁵/₆₆₃	0.15 ⁸⁶/₅₈₆	0.14 ¹²⁹/₉₅₁	0.16 ²¹⁶/₁₃₅₆	0.13 ²⁷⁴/₂₁₄₀	0.10 ¹⁰⁰⁸/₁₀₃₄₆
a b c represent the lower quartile a, the median b, and the upper quartile c for continuous variables. x ± s represents X ± 1 SD. N is the number of non-missing values.

Distribution of age by Glasgow coma score

Distribution of age by gcs

Distribution of systolic blood pressure by Glasgow coma score

Distribution of systolic blood pressure by gcs

Distribution of heart rate by Glasgow coma score

Distribution of heart rate by gcs

Distribution of respiratory rate by Glasgow coma score

Distribution of respiratory rate by GCS

Distribution of central capillary refille time by Glasgow coma score

Distribution of central capillary refill time by GCS

Section session info

## R version 4.0.2 (2020-06-22)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 18363)
## 
## Matrix products: default
## 
## locale:
## [1] LC_COLLATE=English_United States.1252 
## [2] LC_CTYPE=English_United States.1252   
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C                          
## [5] LC_TIME=English_United States.1252    
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] patchwork_1.1.1 corrplot_0.84   gtsummary_1.3.6 Hmisc_4.5-0    
##  [5] Formula_1.2-4   survival_3.1-12 lattice_0.20-41 plotly_4.9.3   
##  [9] forcats_0.5.1   stringr_1.4.0   dplyr_1.0.4     purrr_0.3.4    
## [13] readr_1.4.0     tidyr_1.1.2     tibble_3.0.6    ggplot2_3.3.3  
## [17] tidyverse_1.3.0 here_1.0.1     
## 
## loaded via a namespace (and not attached):
##  [1] fs_1.5.0            usethis_2.0.1       lubridate_1.7.9.2  
##  [4] RColorBrewer_1.1-2  httr_1.4.2          rprojroot_2.0.2    
##  [7] tools_4.0.2         backports_1.2.1     R6_2.5.0           
## [10] rpart_4.1-15        DBI_1.1.1           lazyeval_0.2.2     
## [13] colorspace_2.0-0    nnet_7.3-14         withr_2.4.1        
## [16] tidyselect_1.1.0    gridExtra_2.3       compiler_4.0.2     
## [19] cli_2.3.0           rvest_0.3.6         gt_0.2.2           
## [22] htmlTable_2.1.0     xml2_1.3.2          sass_0.3.1         
## [25] labeling_0.4.2      bookdown_0.21       scales_1.1.1       
## [28] checkmate_2.0.0     commonmark_1.7      digest_0.6.27      
## [31] foreign_0.8-80      rmarkdown_2.6       base64enc_0.1-3    
## [34] jpeg_0.1-8.1        pkgconfig_2.0.3     htmltools_0.5.1.1  
## [37] dbplyr_2.1.0        highr_0.8           htmlwidgets_1.5.3  
## [40] rlang_0.4.10        readxl_1.3.1        rstudioapi_0.13    
## [43] generics_0.1.0      farver_2.0.3        jsonlite_1.7.2     
## [46] crosstalk_1.1.1     magrittr_2.0.1      Matrix_1.2-18      
## [49] Rcpp_1.0.6          munsell_0.5.0       lifecycle_0.2.0    
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## [64] latticeExtra_0.6-29 data.table_1.13.6   broom.helpers_1.1.0
## [67] modelr_0.1.8        png_0.1-7           vctrs_0.3.6        
## [70] rmdformats_1.0.1    cellranger_1.1.0    gtable_0.3.0       
## [73] assertthat_0.2.1    xfun_0.20           broom_0.7.4        
## [76] viridisLite_0.3.0   cluster_2.1.0       ellipsis_0.3.1

NHANES

Introduction to NHANES

Hypothetical research aim for IDA is to develop a multivariable model for MVPA (minutes of moderate/vigorous physical activity) with primary aim of variable selection to predict MVPA and secondary aim to study the role of systolic blood pressure in addition to variables identified. MVPA can be used to examine factors distinguishing very active participants with large amounts of time spent on MVPA from others (using untransformed data) or distinguishing participants according to percentage changes in MVPA (logarithmic scale) thus de-emphasizing extreme values.

NHANES Description

The National Health and Nutrition Examination Survey (NHANES) is a program of studies designed to assess the health and nutritional status of adults and children in the United States. The survey examines a nationally representative sample of non-institutionalized US civilians using a multistage probability sampling design that considers geographical area and minority representation. Sample weights are generated to create nationally representative estimates for the US population and subgroups defined by age, sex, and race/ethnicity. Link to CDC NHANES website. NHANES collects data on various health and behavior indicators, including physical activity and self‐reported diagnosis of prevalent health conditions such as diabetes mellitus, coronary artery disease, stroke, and cancer.

Physical activity was measured with a waist‐worn uniaxial accelerometer (AM‐7164; ActiGraph) for up to 7 days. Participants were asked to wear the devie while awake except when simming or bathing. Data were cleaned according to calibration specification and nonwear time defined by an interval of at least 60 consecutive minutes of zero activity intensity counts. Days with fewer than 10 hours of wear time were excluded and participants with at least 1 valid day of accelerometer data were included in the analysis. Mean counts per minute were calculated by dividing the sum of activity counts for a valid day by the number of minutes of wear time in that day across all valid days. (Troiano 2008)

Moderate or vigorous intensity was based on count thresholds. Time spent in such activities was determined by summing minutes in a day where the count met the criterion for that intensity.(Troiano 2008)

The NHANES 2003–2004 and 2005–2006 have a total of 14,631 participants with accelerometry data. Participants aged 30 to 85 at the time they wore the accelerometer are included. Other inclusion criteria are in line with the choices for the prediction model of 5 year mortality presented by Smirnova et al, J Gerontol A Biol Sci Med Sci 2020. The preparation of the data was based on “Organizing and Analyzing the Activity Data in NHANES” Leroux et al, Statistics in Biosciences 2019. High quality processed activity data combined with mortality and demographic information can be downloaded and used in R with code from Andrew Leroux (https://andrew-leroux.github.io/rnhanesdata/articles).

Preparations

High quality processed activity data combined with mortality and demographic information can be downloaded and used in R with code from Andrew Leroux (https://andrew-leroux.github.io/rnhanesdata/articles). The R code was modified to have fewer exclusions criteria as noted below.

Re-level comorbidities to assign refused/don’t know as not having the condition
Re-level education to have 3 levels and categorize don’t know/refused to be missing
Re-level alcohol consumption to include a level set to missing
Removed the “bad” days from Act_Analysis and Act_Flags
Systolic blood pressure is the mean of the non-missing of four blood pressure variables
Following Smirnova et al, participants were excluded who

had fewer than 3 days of data with at least 10 hours of estimated wear time or were deemed by NHANES to have poor quality data; non-wear periods were identified as intervals with at least 60 consecutive minutes of zero activity counts and at most 2 minutes with counts between 0 and 100;
missing mortality information or accidental death;
alive with follow up less than 1 year

The NHANES dataset used in this project contains 6680 participants.

For the purposes of this IDA project, in contrast to Smirnova et al, we did not exclude participants who

had missing body mass index (BMI) or education predictor variables ;
had missing systolic blood pressure, total or high-density lipoproteins (HDL) cholesterol measurements. The final data set in Smirnova et al contained 2,978 participants.

Sources

Leroux A. Vignettes for downloading and working with NHANES 2003-2004 and 2005-2006 accelerometry data https://andrew-leroux.github.io/rnhanesdata/articles/

To download the analysis data set, click the link to data set —GITHUB

Data dictionary

The data dictionary can be found LINK —- GITHUB

References

Troiano RP, Berrigan D, Dodd KW, Mâsse LC, Tilert T, McDowell M. Physical activity in the United States measured by accelerometer. Med Sci Sports Exerc. 2008 Jan;40(1):181-8. doi: 10.1249/mss.0b013e31815a51b3. PMID: 18091006.

Leroux A, Di J, Smirnova E, Mcguffey E, Cao Q, Bayatmokhtari E, Tabacu L, Zipunnikov V, Urbanek JK, Crainiceanu C. Organizing and Analyzing the Activity Data in NHANES. Stat Biosci 11, 262–287 (2019). https://doi-org.proxy1.cl.msu.edu/10.1007/s12561-018-09229-9

Smirnova E, Leroux A, Tabacu L, Zipunnikov V, Crainiceanu C, Urbanek JK. The Predictive Performance of Objective Measures of Physical Activity Derived From Accelerometry Data for 5-Year All-Cause Mortality in Older Adults: National Health and Nutritional Examination Survey 2003–2006, The Journals of Gerontology: Series A, Volume 75, Issue 9, September 2020, Pages 1779–1785, https://doi.org/10.1093/gerona/glz193

NHANES dataset contents

Source dataset

We refer to the source data set as the dataset available online here

Display the source dataset contents. This dataset is in the data-raw folder of the project directory.

Data frame:nhanesdat

6680 observations and 58 variables, maximum # NAs:5529

Name	Levels	Storage	NAs
seqn		integer	0
paxcal		integer	0
paxstat		integer	0
weekday		integer	0
sddsrvyr		double	0
eligstat		integer	0
mortstat		integer	9
permth.exm		integer	9
sdmvpsu		double	0
sdmvstra		double	0
wtint2yr		double	0
wtmec2yr		double	0
ridagemn		double	0
ridageex		double	0
ridageyr		double	0
bmi		double	56
bmi.cat	4	integer	56
race	5	integer	0
gender	2	integer	0
diabetes	2	integer	0
chf	2	integer	0
chd	2	integer	0
cancer	2	integer	0
stroke	2	integer	0
educationadult	3	integer	7
mobilityproblem	2	integer	0
drinkstatus	4	integer	0
drinksperweek		double	466
smokecigs	3	integer	4
bpxsy1		double	972
bpxsy2		double	1224
bpxsy3		double	1296
bpxsy4		double	5529
lbxtc		double	270
lbdhdd		double	270
age		double	0
sys		double	320
tac		double	708
tlac		double	708
wt		double	708
st		double	708
mvpa		double	708
about		double	708
sbout		double	708
satp		double	708
astp		double	708
tlac.1		double	708
tlac.2		double	708
tlac.3		double	708
tlac.4		double	708
tlac.5		double	708
tlac.6		double	708
tlac.7		double	708
tlac.8		double	708
tlac.9		double	708
tlac.10		double	708
tlac.11		double	708
tlac.12		double	708

Variable	Levels
bmi.cat	Normal
	Underweight
	Overweight
	Obese
race	White
	Mexican American
	Other Hispanic
	Black
	Other
gender	Male
	Female
diabetes, chf, chd	No
cancer, stroke	Yes
educationadult	Less than high school
	High school
	More than high school
mobilityproblem	No Difficulty
	Any Difficulty
drinkstatus	Moderate Drinker
	Non-Drinker
	Heavy Drinker
	Missing alcohol
smokecigs	Never
	Former
	Current

Updated analysis dataset

Additional meta-data is added to the original source data set. We write this new modified data set back to the data folder after adding additional meta-data for the following variables:

seqn - add label “respondent sequence number”
gender - add label "gender’,
age - add label “age” and unit “years”
educationadult - add label “education level”
permth.exm - add label “Person Months of Follow-up from MEC/Exam Date”
mortstat - add label “Final mortality status”
sys - add label “Systolic Blood pressure” and unit “mg/dl”
lbxtc - add label “Total cholesterol” and unit “mg/dL”
lbdhdd - add label “HDL cholesterol” and unit “mg/dL”
smokecigs - add label “smoking status”
drinkstatus - add label “alcohol consumption”
bmi - add label “body mass index” and unit “kg/m2”
diabetes - add label “diabetes”
chf - add label “congestive heart failure”
cancer - add label “cancer”
stroke - add label “stroke”
mobilityproblem - add label “’difficulties with mobility”
tac - add label “total activity counts per day”
tlac - add label “total log activity count (log(1+activity))”
wt - add label “total accelerometer wear time” and unit “minutes”
mvpa - add label “Moderate or vigorous physical activity” and unit “minutes”

At this stage we select the variables of interest to take in to the IDA phase by dropping variables we do not check in IDA.

As a cross check we display the contents again to ensure the additional data is added, and then write back the changes to the data folder in the file “data/a_nhanes.rda”.

Input object size: 1479216 bytes; 33 variables 6680 observations New object size: 1416624 bytes; 33 variables 6680 observations

Data frame:a_nhanes

6680 observations and 33 variables, maximum # NAs:708

Name	Labels	Units	Levels	Class	Storage	NAs
seqn	respondent sequence number			integer	integer	0
age	age	years		numeric	double	0
gender	gender		2		integer	0
permth.exm	Person Months of Follow-up from MEC/Exam Date			integer	integer	9
mortstat	Final mortality status			integer	integer	9
educationadult	education level		3		integer	7
smokecigs	smoking status		3		integer	4
drinkstatus	alcohol consumption		4		integer	0
bmi	body mass index	kg/m2		numeric	double	56
diabetes	diabetes		2		integer	0
chf	congestive heart failure		2		integer	0
cancer	cancer		2		integer	0
stroke	stroke		2		integer	0
sys	Systolic blood pressure	mg/dl		integer	integer	320
lbxtc	Total cholesterol	mg/dL		integer	integer	270
lbdhdd	HDL cholesterol	mg/dL		integer	integer	270
mobilityproblem	difficulties with mobility		2		integer	0
tac	total activity counts per day			numeric	double	708
tlac	total log activity count (log(1+activity))			numeric	double	708
mvpa	Moderate or vigorous physical activity	minutes		numeric	double	708
wt	total accelerometer wear time	minutes		numeric	double	708
tlac.1	total log actvity count 12:00AM-2:00AM			numeric	double	708
tlac.2	total log actvity count 2:00AM-4:00AM			numeric	double	708
tlac.3	total log actvity count 4:00AM-6:00AM			numeric	double	708
tlac.4	total log actvity count 6:00AM-8:00AM			numeric	double	708
tlac.5	total log actvity count 8:00AM-10:00AM			numeric	double	708
tlac.6	total log actvity count 10:00AM-12:00PM			numeric	double	708
tlac.7	total log actvity count 12:00PM-2:00PM			numeric	double	708
tlac.8	total log actvity count 2:00PM-4:00PM			numeric	double	708
tlac.9	total log actvity count 4:00PM-6:00PM			numeric	double	708
tlac.10	total log actvity count 6:00PM-8:00PM			numeric	double	708
tlac.11	total log actvity count 8:00PM-10:00PM			numeric	double	708
tlac.12	total log actvity count 10:00PM-12:00AM			numeric	double	708

Variable	Levels
gender	Male
	Female
educationadult	Less than high school
	High school
	More than high school
smokecigs	Never
	Former
	Current
drinkstatus	Moderate Drinker
	Non-Drinker
	Heavy Drinker
	Missing alcohol
diabetes, chf	No
cancer, stroke	Yes
mobilityproblem	No Difficulty
	Any Difficulty

Section session info

## R version 4.0.2 (2020-06-22)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 18363)
## 
## Matrix products: default
## 
## locale:
## [1] LC_COLLATE=English_United States.1252 
## [2] LC_CTYPE=English_United States.1252   
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C                          
## [5] LC_TIME=English_United States.1252    
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] Hmisc_4.5-0     Formula_1.2-4   survival_3.1-12 lattice_0.20-41
##  [5] forcats_0.5.1   stringr_1.4.0   dplyr_1.0.4     purrr_0.3.4    
##  [9] readr_1.4.0     tidyr_1.1.2     tibble_3.0.6    ggplot2_3.3.3  
## [13] tidyverse_1.3.0 here_1.0.1     
## 
## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.6          lubridate_1.7.9.2   png_0.1-7          
##  [4] assertthat_0.2.1    rprojroot_2.0.2     digest_0.6.27      
##  [7] R6_2.5.0            cellranger_1.1.0    backports_1.2.1    
## [10] reprex_1.0.0        evaluate_0.14       httr_1.4.2         
## [13] pillar_1.4.7        rlang_0.4.10        readxl_1.3.1       
## [16] data.table_1.13.6   rstudioapi_0.13     rpart_4.1-15       
## [19] Matrix_1.2-18       checkmate_2.0.0     rmarkdown_2.6      
## [22] splines_4.0.2       foreign_0.8-80      htmlwidgets_1.5.3  
## [25] munsell_0.5.0       broom_0.7.4         compiler_4.0.2     
## [28] modelr_0.1.8        xfun_0.20           pkgconfig_2.0.3    
## [31] base64enc_0.1-3     htmltools_0.5.1.1   nnet_7.3-14        
## [34] tidyselect_1.1.0    htmlTable_2.1.0     gridExtra_2.3      
## [37] bookdown_0.21       crayon_1.4.1        dbplyr_2.1.0       
## [40] withr_2.4.1         grid_4.0.2          jsonlite_1.7.2     
## [43] gtable_0.3.0        lifecycle_0.2.0     DBI_1.1.1          
## [46] magrittr_2.0.1      scales_1.1.1        rmdformats_1.0.1   
## [49] cli_2.3.0           stringi_1.5.3       fs_1.5.0           
## [52] latticeExtra_0.6-29 xml2_1.3.2          ellipsis_0.3.1     
## [55] generics_0.1.0      vctrs_0.3.6         RColorBrewer_1.1-2 
## [58] tools_4.0.2         glue_1.4.2          hms_1.0.0          
## [61] jpeg_0.1-8.1        yaml_2.2.1          colorspace_2.0-0   
## [64] cluster_2.1.0       rvest_0.3.6         knitr_1.31         
## [67] haven_2.3.1

Statistical analysis plan

Hypothetical research aim for IDA: The primary aim is to develop a multivariable model for MVPA (minutes of moderate/vigorous physical activity) with primary aim of variable selection to predict MVPA. Specifcially, the role of gender and age will be investigated. A secondary aim to study the role of systolic blood pressure in addition to variables identified. MVPA can be used to examine factors distinguishing very active participants with large amounts of time spent on MVPA from others (using untransformed data) or distinguishing participants according to percentage changes in MVPA (logarithmic scale) thus de-emphasizing extreme values.

The inclusion criteria are in line with the choices for the prediction model of 5 year mortality presented by Smirnova et al, J Gerontol A Biol Sci Med Sci 2020.

Statistical methods

Linear regression models will be used to model MVPA. Explanatory variables are age, gender, education, smoking, alcohol consumption, BMI, comorbidities (cancer, CHF, stroke), cholesterol (total, HDL). Partial R-squared will be used to identify an appropriate set of variables to predict MVPA. A secondary aim is to study the role of systolic blood pressure on MVPA in a linear regression model with variables identified in the previous step.

Variables

Outcome variable

MVPA (total minutes of moderate/vigorous physical activity which is defined as more than 2020 counts per minute) (mvpa, minutes)

Sociodemographic variables

age at examination (i.e. when participants wore the device) (age, years)
gender (gender, “Male” and “Female”)
race/ethnicity (non-Hispanic “White”, non-Hispanic “Black”, “Mexican American”, and “Other”)
education (“Less than high school”, “High school” (high school graduate/general educational development [GED]), “More than high school” (some college, and college graduate)) (educationadult)
5 year mortality, NAs for individuals with follow up less than 5 years and alive (yr5.mort)
Person Months of Follow-up from MEC/Exam Date (permth.exm) (follow-up time in this cohort in years = permth.exm/12)
final mortality status (mortstat, 0, 1, NAs for individuals with follow up less than 5 years and alive)

Health and behavior variables

smoking status (Current, Former [those reporting quitting within the previous 6 months], and Never) (smokecigs)
alcohol consumption (drinkstatus) (Non-Drinker, Moderate Drinker, Heavy Drinker, Missing alcohol)
bmi (bmi, kg/m2)
obesity (bmi.cat, No-Yes)
diabetes (diabetes)
congestive heart failure (chf, No-Yes)
cancer (cancer, No-Yes)
stroke (stroke, No-Yes)
average systolic blood pressure using the 4 measurements per participant (sys, mmHg)
Total cholesterol (lbxtc, mg/dL)
HDL cholesterol (lbdhdd, mg/dL)
difficulties with mobility (mobilityproblem, “No Difficulty”, “Any Difficulty” = a positive response to difficulty walking a quarter-mile, difficulty climbing 10 stairs, or use of any special equipment to walk)

Physical activity data

Summary measures are calculated due to the large size of minute level accelerometer-derived physical activity data.

total activity counts per day (TAC/d)
total log activity count (TLAC log(1+TAC))
total minutes of moderate/vigorous physical activity (MVPA)
total accelerometer wear time (WT)
total log activity count summary measures (tlac.1,tlac.2, …,tlac.12`) in each 2-hr window, i.e. 12AM-2AM, 2AM-4AM, 4AM-6AM, etc.

Initial data analysis strategy

1. Statistical analysis plan: as assumed above, the analysis strategy to answer the main research question has been prespecified. It comprises of the set of independent variables to be considered in a model, the outcome variable, and the analytical strategy to build the regression model.

SAP is listed above

2. Data dictionary and metadata: a detailed data dictionary should be available which informs about the meaning of each variable in context of the research question, the units of measurement, the possible levels in case of categorical variables, or admissible values. More generally, metadata, also refer to information about the research study protocol and data collection processes.

A data dictionary is available.

3. Domain expertise and pivotal covariates (‘very important predictors’, VIPs)

It has been shown that physcial activity declines with age and men report higher levels of activity than women. Age and gender, also defined in the research aim, are pivotal covariates.

Keadle S et al. Prevalence and trends in physical activity among older adults in the United States: A comparison across three national surveys. Prev Med. 2016 Aug; 89: 37–43. https://doi.org/10.1016/j.ypmed.2016.05.009

Clarke TC, Norris T, and Schiller JS. Early Release of Selected Estimates Based on Data From the 2018 National Health Interview Survey. https://www.cdc.gov/nchs/nhis/releases/released201905.htm#7a

3.2. Domain expertise may also be useful to specify in advance which variables are expected to correlate with each other. This background knowledge could be summarized in a directed or undirected acyclic graph connecting the covariates with each other as also suggested by Heinze et al, 2018.

3.3. Missing value mechanisms: if not already specified in meta data, domain experts should also be consulted to explain possible reasons for the occurrence of missing values for each variable, which may be categorized as systematic or unsystematic.

Missing values are expected due to the nature of survey research. Domain expertice would be helpful in identifying specific expectations. Missingness of some covariates may be associated with the outcome variable. This will be considered in the IDA domain ‘Missing values’ to identify approaches or updates to the SAP.

IDA domain: missing values

1. Number and proportion of missing values for each independent variable, for the dependent variable and for the analysis as a whole.

Number and proportion of missing values will be computed for all variables.

2. Patterns of missing values across all independent variables, either as tables or appropriately visualized.

We will create missing value indicators for each covariate and will then summarize patterns by means of a heat map and a dendogram.

3. Patterns of missing values associated with the outcome variable

This may need to change.

From Lee at al (STRATOS)

A table of the observed characteristics for the “complete” versus “incomplete” (or all) participants, or by whether variables with substantial missingness are observed.
An assessment of the predictors of missingness, e.g. using a logistic regression model fitted to an indicator for being a complete record, and predictors of missing values i.e. associations with the incomplete variables.

IDA domain: univariate distributions

3. For categorical variables (including the dependent variable): frequency and proportion for each category.

Demographic variables, smoking status, alcohol consumption, comorbidities, and mortality status will be described by frequencies and proportions.

4. For continuous variables (including the dependent variable): high-resolution histogram, summary of main percentiles (1st, 10th, 25th, 50th, 75th, 90th, 99th) and interquartile range, 5 highest and 5 lowest values, first four moments (mean, variance, skewness, curtosis), standard deviation, number of distinct values.

Summaries for all continuous variables (age, BMI, physiological variables, physical activity) will be created to depict their marginal distributions by means of high-resolution histograms. Furthermore, each continuous variable will be described by 1st, 10th, 25th, 50th, 75th, 90th, 99th percentiles, interquartile range, the 5 highest and 5 lowest values, the first four moments (mean, variance, skewness, curtosis), standard deviation, and the number of distinct values.

While the outcome variable MVPA is the only physical activity variable in the analysis plan, since it is a derived variables from some of the other physical activity variables, others will be looked at in the univariate step to identify potential issues of skewness or unusual values.

The graphical summary for each variable will serve to suggest transformations for each variable:

no transformation (in case of approximate symmetry);
\(\log_{10}(x+1)\) transformation (in case of skewness)

The distributions of transformed variables will be evaluated as well as described above.

It is assumed that the data have been cleaned, but unusual values will be identified and possibly excluded.

IDA domain: multivariate system of variables

5. Matrix/heatmap of Pearson correlation coefficients between all independent variables.

Pearson correlation coefficients will be computed between all independent variables. The correlation coefficients will be depicted by means of a (quadratic) heat map. Moreover, a network graph between all independent variables will be constructed, which will be thresholded at an absolute correlation coefficient of 0.3.

Spearman correlation coefficients will be computed as well, and the 10 pairs of covariates with the largest absolute difference between Pearson and Spearman correlation coefficients will be flagged. These pairs will be graphically investigated by constructing separate scatterplots.

6. Appropriate visual (and numerical) presentations of the association of each covariate with the two pivotal covariates.

A redundancy analysis will be conducted for each variable. This analysis identifies predictors that can be almost perfectly predicted by flexible parametric additive models performed on the companion covariates.

Categorical and continuous variables will be summarized with counts and proportions or medians and quartiles, as appropriate, in a table stratified by sex and age groups.

Scatterplots of continuous variables by age will be constructed stratified by gender.

7. If interactions between covariates were prespecified to be included in the regression model, special attention should be given to evaluate the bivariate distribution of the interacting covariates. Appropriate graphical displays (see 6) should be used to visualise these distributions.

Interactions between age and gender will be considered. The distribution of age will be depicted as histogram stratified for gender.

8. For a derived outcome variable, the bivariate distribution of these variables with the outcome variable should be evaluated with appropriate visualizations..

Scatter plots of the physical activity variables with MVPA will be constructed with trend lines.

Missing data

Per variable missingness

Number and percentage of missing.

Variable	Missing (count)	Missing (%)
tac	708	10.60
tlac	708	10.60
mvpa	708	10.60
wt	708	10.60
tlac.1	708	10.60
tlac.2	708	10.60
tlac.3	708	10.60
tlac.4	708	10.60
tlac.5	708	10.60
tlac.6	708	10.60
tlac.7	708	10.60
tlac.8	708	10.60
tlac.9	708	10.60
tlac.10	708	10.60
tlac.11	708	10.60
tlac.12	708	10.60
sys	320	4.79
lbxtc	270	4.04
lbdhdd	270	4.04
bmi	56	0.84
permth.exm	9	0.13
mortstat	9	0.13
educationadult	7	0.10
smokecigs	4	0.06
age	0	0.00
gender	0	0.00
drinkstatus	0	0.00
diabetes	0	0.00
chf	0	0.00
cancer	0	0.00
stroke	0	0.00
mobilityproblem	0	0.00

Variable summaries for complete vs incomplete cases

Participant characteristics by missing status of MVPA
	complete (N=708)	incomplete (N=5972)	Total (N=6680)	p value
age				< 0.001
Median	48.375	53.750	53.167
Q1, Q3	38.583, 64.271	41.646, 67.250	41.333, 67.000
Range	30.000 - 84.917	30.000 - 84.917	30.000 - 84.917
gender				0.432
Male	359 (50.7%)	2935 (49.1%)	3294 (49.3%)
Female	349 (49.3%)	3037 (50.9%)	3386 (50.7%)
education level				0.072
N-Miss	3	4	7
Less than high school	216 (30.6%)	1683 (28.2%)	1899 (28.5%)
High school	186 (26.4%)	1448 (24.3%)	1634 (24.5%)
More than high school	303 (43.0%)	2837 (47.5%)	3140 (47.1%)
body mass index				0.796
Median	28.400	28.080	28.100
Q1, Q3	24.373, 32.353	24.730, 32.230	24.718, 32.250
Range	16.570 - 72.280	13.360 - 130.210	13.360 - 130.210
smoking status				0.051
N-Miss	2	2	4
Never	342 (48.4%)	2911 (48.8%)	3253 (48.7%)
Former	185 (26.2%)	1759 (29.5%)	1944 (29.1%)
Current	179 (25.4%)	1300 (21.8%)	1479 (22.2%)
alcohol consumption				0.008
Moderate Drinker	359 (50.7%)	3090 (51.7%)	3449 (51.6%)
Non-Drinker	238 (33.6%)	2098 (35.1%)	2336 (35.0%)
Heavy Drinker	40 (5.6%)	389 (6.5%)	429 (6.4%)
Missing alcohol	71 (10.0%)	395 (6.6%)	466 (7.0%)
Final mortality status				0.205
Median	0.000	0.000	0.000
Q1, Q3	0.000, 0.000	0.000, 0.000	0.000, 0.000
Range	0.000 - 1.000	0.000 - 1.000	0.000 - 1.000
diabetes				0.659
No	614 (86.7%)	5214 (87.3%)	5828 (87.2%)
Yes	94 (13.3%)	758 (12.7%)	852 (12.8%)
congestive heart failure				0.538
No	677 (95.6%)	5739 (96.1%)	6416 (96.0%)
Yes	31 (4.4%)	233 (3.9%)	264 (4.0%)
cancer				0.106
No	649 (91.7%)	5359 (89.7%)	6008 (89.9%)
Yes	59 (8.3%)	613 (10.3%)	672 (10.1%)
stroke				0.163
No	672 (94.9%)	5734 (96.0%)	6406 (95.9%)
Yes	36 (5.1%)	238 (4.0%)	274 (4.1%)
Systolic blood pressure				0.090
Median	123.000	124.000	124.000
Q1, Q3	113.000, 135.000	113.000, 138.000	113.000, 138.000
Range	82.000 - 228.000	73.000 - 270.000	73.000 - 270.000
Total cholesterol				0.394
Median	199.000	201.000	201.000
Q1, Q3	172.000, 229.000	175.000, 228.000	175.000, 229.000
Range	99.000 - 704.000	82.000 - 650.000	82.000 - 704.000
HDL cholesterol				0.260
Median	50.000	52.000	52.000
Q1, Q3	42.000, 63.000	43.000, 64.000	42.000, 63.000
Range	17.000 - 164.000	17.000 - 188.000	17.000 - 188.000
difficulties with mobility				0.817
No Difficulty	542 (76.6%)	4595 (76.9%)	5137 (76.9%)
Any Difficulty	166 (23.4%)	1377 (23.1%)	1543 (23.1%)
total log activity count (log(1+activity))
Median	NA	2910.926	2910.926
Q1, Q3	NA	2384.757, 3430.648	2384.757, 3430.648
Range	NA	313.083 - 6122.678	313.083 - 6122.678
total accelerometer wear time
Median	NA	852.071	852.071
Q1, Q3	NA	782.851, 922.036	782.851, 922.036
Range	NA	600.000 - 1440.000	600.000 - 1440.000

It appears that participants with incomplete physical activity data are older.

Missingness patterns over variables

(In)complete cases

This section presents patients with a least one missing value. First we list out patients with at least one missing value in a filterable table.

Then we report the pattern of missing for this set of patients.

Section session info

## R version 4.0.2 (2020-06-22)
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## [4] LC_NUMERIC=C                          
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## 
## attached base packages:
## [1] grid      stats     graphics  grDevices utils     datasets  methods  
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##  [9] Formula_1.2-4    survival_3.1-12  lattice_0.20-41  forcats_0.5.1   
## [13] stringr_1.4.0    dplyr_1.0.4      purrr_0.3.4      readr_1.4.0     
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## [13] xml2_1.3.2          splines_4.0.2       robustbase_0.93-7  
## [16] knitr_1.31          jsonlite_1.7.2      broom_0.7.4        
## [19] cluster_2.1.0       dbplyr_2.1.0        png_0.1-7          
## [22] compiler_4.0.2      httr_1.4.2          backports_1.2.1    
## [25] assertthat_0.2.1    Matrix_1.2-18       cli_2.3.0          
## [28] htmltools_0.5.1.1   tools_4.0.2         gtable_0.3.0       
## [31] glue_1.4.2          Rcpp_1.0.6          carData_3.0-4      
## [34] cellranger_1.1.0    vctrs_0.3.6         crosstalk_1.1.1    
## [37] lmtest_0.9-38       xfun_0.20           laeken_0.5.1       
## [40] openxlsx_4.2.3      rvest_0.3.6         lifecycle_0.2.0    
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## [55] latticeExtra_0.6-29 stringi_1.5.3       highr_0.8          
## [58] e1071_1.7-4         checkmate_2.0.0     boot_1.3-25        
## [61] zip_2.1.1           rlang_0.4.10        pkgconfig_2.0.3    
## [64] commonmark_1.7      evaluate_0.14       htmlwidgets_1.5.3  
## [67] labeling_0.4.2      tidyselect_1.1.0    plyr_1.8.6         
## [70] magrittr_2.0.1      bookdown_0.21       R6_2.5.0           
## [73] generics_0.1.0      DBI_1.1.1           pillar_1.4.7       
## [76] haven_2.3.1         foreign_0.8-80      withr_2.4.1        
## [79] abind_1.4-5         sp_1.4-5            nnet_7.3-14        
## [82] modelr_0.1.8        crayon_1.4.1        car_3.0-10         
## [85] rmarkdown_2.6       jpeg_0.1-8.1        readxl_1.3.1       
## [88] data.table_1.13.6   rmdformats_1.0.1    vcd_1.4-8          
## [91] reprex_1.0.0        digest_0.6.27       webshot_0.5.2      
## [94] munsell_0.5.0       viridisLite_0.3.0

Univariate distribution checks

This section reports a series of univariate summary checks of the NHANES dataset.

## Rows: 6,680
## Columns: 33
## $ seqn            <labelled> 21009, 21010, 21012, 21015, 21017, 21018, 2101...
## $ age             <labelled> 56.00000, 52.83333, 63.83333, 83.91667, 37.083...
## $ gender          <fct> Male, Female, Male, Male, Female, Female, Female, F...
## $ permth.exm      <labelled> 135, 149, 127, 24, 151, 154, 153, 154, 141, 14...
## $ mortstat        <labelled> 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0...
## $ educationadult  <fct> High school, More than high school, High school, Mo...
## $ smokecigs       <fct> Never, Current, Current, Former, Current, Never, Fo...
## $ drinkstatus     <fct> Non-Drinker, Heavy Drinker, Missing alcohol, Non-Dr...
## $ bmi             <labelled> 31.26, 25.49, 19.60, 28.32, 19.34, 16.57, 38.0...
## $ diabetes        <fct> No, No, No, No, No, No, No, No, No, No, No, No, Yes...
## $ chf             <fct> No, No, No, No, No, No, Yes, No, No, No, No, No, No...
## $ cancer          <fct> No, No, No, Yes, No, No, No, No, No, No, Yes, No, N...
## $ stroke          <fct> No, No, No, No, No, No, No, No, No, No, No, No, No,...
## $ sys             <labelled> 120, 133, 123, 154, 103, 137, 115, 131, 121, 1...
## $ lbxtc           <labelled> 254, 174, 191, 141, 184, NA, 173, 230, 261, 21...
## $ lbdhdd          <labelled> 37, 119, 92, 34, 77, NA, 45, 51, 29, 68, 53, 4...
## $ mobilityproblem <fct> No Difficulty, No Difficulty, Any Difficulty, Any D...
## $ tac             <labelled> 409352.71, 286407.71, 130778.29, 102562.86, 41...
## $ tlac            <labelled> 3522.427, 3334.503, 2749.086, 2103.580, 3689.4...
## $ mvpa            <labelled> 48.285714, 9.428571, 4.714286, 3.000000, 58.83...
## $ wt              <labelled> 900.2857, 783.4286, 1053.0000, 813.1429, 833.8...
## $ tlac.1          <labelled> 0.0000000, 0.0000000, 161.7450224, 5.6786074, ...
## $ tlac.2          <labelled> 0.000000, 0.000000, 128.091725, 7.244960, 0.00...
## $ tlac.3          <labelled> 66.563485, 0.000000, 145.091848, 8.942295, 0.0...
## $ tlac.4          <labelled> 476.33325, 0.00000, 74.34726, 18.38650, 459.83...
## $ tlac.5          <labelled> 612.21257, 358.95003, 152.73994, 106.23999, 57...
## $ tlac.6          <labelled> 586.1977, 449.0983, 249.8184, 286.1406, 571.73...
## $ tlac.7          <labelled> 462.8831, 514.9402, 352.7644, 393.9136, 637.96...
## $ tlac.8          <labelled> 587.5167, 550.7981, 277.3621, 321.9635, 634.96...
## $ tlac.9          <labelled> 315.9585, 487.6278, 302.4908, 327.1102, 254.62...
## $ tlac.10         <labelled> 251.4170, 527.7868, 310.0226, 313.5571, 338.45...
## $ tlac.11         <labelled> 159.78640, 401.07109, 312.24852, 254.92505, 19...
## $ tlac.12         <labelled> 3.558282, 44.230766, 282.363630, 59.477670, 26...

Data set overview

Demographic and lifestyle variables

Demographic and lifestyle variables

6 Variables 5972 Observations

age years

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	660	1	54.87	17.64	32.17	34.58	41.65	53.75	67.25	76.50	80.83

lowest : 30.00000 30.08333 30.16667 30.25000 30.33333 , highest: 84.58333 84.66667 84.75000 84.83333 84.91667

gender

n	missing	distinct
5972	0	2

 Value        Male Female
 Frequency    2935   3037
 Proportion  0.491  0.509

educationadult: education level

n	missing	distinct
5968	4	3

 Value      Less than high school           High school More than high school
 Frequency                   1683                  1448                  2837
 Proportion                 0.282                 0.243                 0.475

bmi: body mass index kg/m2

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5928	44	2161	1	29.07	6.804	20.78	22.12	24.73	28.08	32.23	37.07	40.80

lowest : 13.36 14.65 14.70 15.91 15.92 , highest: 62.50 62.77 63.42 63.87 130.21

smokecigs: smoking status

n	missing	distinct
5970	2	3

 Value        Never  Former Current
 Frequency     2911    1759    1300
 Proportion   0.488   0.295   0.218

drinkstatus: alcohol consumption

n	missing	distinct
5972	0	4

 Value      Moderate Drinker      Non-Drinker    Heavy Drinker  Missing alcohol
 Frequency              3090             2098              389              395
 Proportion            0.517            0.351            0.065            0.066

Physiological measurements

Physiological measurements

3 Variables 5972 Observations

sys: Systolic blood pressure mg/dl

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5698	274	137	1	127.4	22.26	100.0	105.0	113.0	124.0	138.0	154.0	166.1

lowest : 73 80 81 83 85 , highest: 226 230 238 256 270

lbxtc: Total cholesterol mg/dL

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5742	230	264	1	204.1	46.4	143	155	175	201	228	258	277

lowest : 82 83 85 92 94 , highest: 431 440 458 539 650

lbdhdd: HDL cholesterol mg/dL

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5742	230	109	1	54.64	17.91	33	37	43	52	64	76	85

lowest : 17 22 23 24 25 , highest: 146 151 152 154 188

Comorbidities

Comorbidities

5 Variables 5972 Observations

mortstat: Final mortality status

n	missing	distinct	Info	Sum	Mean	Gmd
5964	8	2	0.441	1068	0.1791	0.2941

diabetes

n	missing	distinct
5972	0	2

 Value         No   Yes
 Frequency   5214   758
 Proportion 0.873 0.127

chf: congestive heart failure

n	missing	distinct
5972	0	2

 Value         No   Yes
 Frequency   5739   233
 Proportion 0.961 0.039

cancer

n	missing	distinct
5972	0	2

 Value         No   Yes
 Frequency   5359   613
 Proportion 0.897 0.103

stroke

n	missing	distinct
5972	0	2

 Value        No  Yes
 Frequency  5734  238
 Proportion 0.96 0.04

Physical activity variables

Physical activity

17 Variables 5972 Observations

mobilityproblem: difficulties with mobility

n	missing	distinct
5972	0	2

 Value       No Difficulty Any Difficulty
 Frequency            4595           1377
 Proportion          0.769          0.231

tac: total activity counts per day

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5965	1	244811	143738	69233	94872	150571	223572	314224	417410	486450

lowest :	8263.000	8931.833	12123.000	14642.000	15656.000
highest:	981517.167	986261.000	986593.800	1097823.500	1122542.600

tlac: total log activity count (log(1+activity))

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5969	1	2900	873.5	1613	1900	2385	2911	3431	3877	4164

lowest :	313.0835	364.4561	400.8157	429.9288	466.0362
highest:	5436.1548	5492.5395	5588.3401	5655.4680	6122.6779

mvpa: Moderate or vigorous physical activity minutes

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	1163	1	19.19	20.9	0.800	1.429	4.000	12.000	26.762	46.000	59.921

lowest :	0.0000000	0.1428571	0.1666667	0.2000000	0.2500000
highest:	180.8333333	186.2000000	194.8000000	208.5000000	249.0000000

wt: total accelerometer wear time minutes

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	3613	1	866.1	139.8	684.3	721.0	782.9	852.1	922.0	1000.6	1111.5

lowest : 600.000 601.500 602.000 603.000 604.000 , highest: 1425.286 1426.250 1426.286 1426.857 1440.000

tlac.1: total log actvity count 12:00AM-2:00AM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	2656	0.829	30.92	51.83	0.00	0.00	0.00	0.00	24.38	94.43	169.25

lowest :	0.0000000	0.1569446	0.1831020	0.2299197	0.2559656
highest:	597.3808309	620.0469233	674.1677375	709.3300116	719.0239316

tlac.2: total log actvity count 2:00AM-4:00AM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	1770	0.653	19.09	34.47	0.00	0.00	0.00	0.00	2.91	51.83	110.64

lowest :	0.00000000	0.09902103	0.11552453	0.15694461	0.23104906
highest:	586.34967162	611.00545824	617.44773130	737.25383394	775.42871350

tlac.3: total log actvity count 4:00AM-6:00AM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	2834	0.855	43.29	70.78	0.00	0.00	0.00	0.00	38.74	147.59	248.43

lowest :	0.0000000	0.1155245	0.1386294	0.2299197	0.2682397
highest:	679.1484297	697.1093552	704.5766819	719.3198459	769.6014301

tlac.4: total log actvity count 6:00AM-8:00AM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5285	0.998	177	178.6	0.00	0.00	36.94	137.34	282.09	416.35	496.25

lowest :	0.0000000	0.2299197	0.3465736	0.6148132	0.6839274
highest:	774.8811640	792.6938042	822.1482092	832.9933042	857.9018816

tlac.5: total log actvity count 8:00AM-10:00AM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5834	1	339.3	191.7	39.52	102.56	221.28	346.74	460.18	552.17	610.19

lowest :	0.0000000	0.2310491	0.7250248	0.8652549	1.0357837
highest:	812.0225306	812.8675420	813.2942210	824.5800445	888.1759271

tlac.6: total log actvity count 10:00AM-12:00PM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5931	1	407.7	163.6	150.4	218.6	316.2	415.0	506.7	589.9	634.9

lowest :	0.0000000	0.6986213	2.6001909	4.5903937	5.7234361
highest:	807.7712473	808.7247458	811.5701740	884.1169241	892.0314653

tlac.7: total log actvity count 12:00PM-2:00PM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5947	1	418	146.9	192.1	250.4	337.6	423.5	507.2	581.3	623.7

lowest :	0.000000	1.734669	2.704424	5.605670	6.387910
highest:	788.370472	796.082067	813.380498	821.733575	885.445891

tlac.8: total log actvity count 2:00PM-4:00PM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5954	1	411.7	147.8	192.1	243.1	323.6	414.3	501.7	577.5	619.9

lowest :	0.000000	1.974752	3.096473	4.094345	5.772020
highest:	792.683985	837.042353	846.553847	877.212734	904.872351

tlac.9: total log actvity count 4:00PM-6:00PM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5955	1	397	140.3	185.4	234.8	316.4	401.8	483.5	553.6	591.4

lowest :	0.000000	2.957040	3.401197	4.148165	5.084134
highest:	771.497952	783.128869	801.039991	809.429425	822.294800

tlac.10: total log actvity count 6:00PM-8:00PM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5932	1	337.6	151.3	114.1	165.5	246.6	339.5	433.1	504.4	548.9

lowest :	0.000000	1.311822	1.353699	1.753975	3.459493
highest:	778.168243	778.774433	802.020060	851.421446	860.123328

tlac.11: total log actvity count 8:00PM-10:00PM

n	missing	distinct	Info	Mean	Gmd	.05	.10	.25	.50	.75	.90	.95
5972	0	5786	1	223.2	158.2	10.22	42.32	116.77	212.72	315.90	411.75	471.84

lowest :	0.0000000	0.6229449	0.6708919	1.0233141	1.0525597
highest:	724.9040071	753.8848070	821.4989318	826.3463412	839.8942777

tlac.12: total log actvity count 10:00PM-12:00AM

        n  missing distinct     Info     Mean      Gmd      .05      .10      .25 
     5972        0     4943    0.995    95.37    114.3    0.000    0.000    6.693 
      .50      .75      .90      .95 
   55.438  141.863  251.308  328.945

lowest :	0.00000000	0.09902103	0.17328680	0.27798716	0.41291025
highest:	683.58618305	698.46723961	702.66304648	707.15487443	733.61717206

Categorical variables

We now provide a closer visual examination of the categorical predictors.

Continuous variables

A closer visual examination of continuous predictors and the outcome variable.

There is evidence of influential points in some of the distributions. This is explored further with targeted summaries. A more detailed univariate summaries for the variables of interest are also provided below.

Outcome= Time of moderate or vigrous physical activity and related variables

## Warning: Removed 15 rows containing missing values (geom_point).

## Warning: Removed 2 rows containing missing values (geom_bar).

Distribution of time of moderate/vigorous activity [minutes]

After transforming MVPA with \(\log_{10}(x+1)\):

## Warning: Removed 17 rows containing missing values (geom_point).

## Warning: Removed 2 rows containing missing values (geom_bar).

Distribution of log(1+MVPA)

## Warning: Removed 10 rows containing missing values (geom_point).

## Warning: Removed 2 rows containing missing values (geom_bar).

Distribution of wear time [minutes]

## Warning: Removed 2 rows containing missing values (geom_bar).

Distribution of log total activity count

Age

## Warning: Removed 5 rows containing missing values (geom_point).

## Warning: Removed 2 rows containing missing values (geom_bar).

Distribution of age

Blood pressure

Distribution of SBP

Body mass index

Distribution of respiratory rate

There is a participant with an unusal high value (130.2). It is possible that this is an entry error (bmi=30.2).

Total cholesterol

Distribution of total cholesterol

Distribution of HDL

Section session info

## R version 4.0.2 (2020-06-22)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 18363)
## 
## Matrix products: default
## 
## locale:
## [1] LC_COLLATE=English_United States.1252 
## [2] LC_CTYPE=English_United States.1252   
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C                          
## [5] LC_TIME=English_United States.1252    
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] Hmisc_4.5-0     Formula_1.2-4   survival_3.1-12 lattice_0.20-41
##  [5] forcats_0.5.1   stringr_1.4.0   dplyr_1.0.4     purrr_0.3.4    
##  [9] readr_1.4.0     tidyr_1.1.2     tibble_3.0.6    ggplot2_3.3.3  
## [13] tidyverse_1.3.0 here_1.0.1     
## 
## loaded via a namespace (and not attached):
##  [1] httr_1.4.2          jsonlite_1.7.2      splines_4.0.2      
##  [4] modelr_0.1.8        assertthat_0.2.1    highr_0.8          
##  [7] latticeExtra_0.6-29 cellranger_1.1.0    yaml_2.2.1         
## [10] pillar_1.4.7        backports_1.2.1     glue_1.4.2         
## [13] digest_0.6.27       RColorBrewer_1.1-2  checkmate_2.0.0    
## [16] rvest_0.3.6         colorspace_2.0-0    htmltools_0.5.1.1  
## [19] Matrix_1.2-18       pkgconfig_2.0.3     broom_0.7.4        
## [22] haven_2.3.1         bookdown_0.21       patchwork_1.1.1    
## [25] scales_1.1.1        jpeg_0.1-8.1        htmlTable_2.1.0    
## [28] generics_0.1.0      farver_2.0.3        ellipsis_0.3.1     
## [31] withr_2.4.1         nnet_7.3-14         cli_2.3.0          
## [34] magrittr_2.0.1      crayon_1.4.1        readxl_1.3.1       
## [37] evaluate_0.14       fs_1.5.0            fansi_0.4.2        
## [40] xml2_1.3.2          foreign_0.8-80      tools_4.0.2        
## [43] data.table_1.13.6   hms_1.0.0           lifecycle_0.2.0    
## [46] munsell_0.5.0       reprex_1.0.0        cluster_2.1.0      
## [49] compiler_4.0.2      rlang_0.4.10        grid_4.0.2         
## [52] rstudioapi_0.13     htmlwidgets_1.5.3   base64enc_0.1-3    
## [55] labeling_0.4.2      rmarkdown_2.6       gtable_0.3.0       
## [58] DBI_1.1.1           R6_2.5.0            gridExtra_2.3      
## [61] lubridate_1.7.9.2   knitr_1.31          utf8_1.1.4         
## [64] rprojroot_2.0.2     stringi_1.5.3       rmdformats_1.0.1   
## [67] Rcpp_1.0.6          vctrs_0.3.6         rpart_4.1-15       
## [70] png_0.1-7           dbplyr_2.1.0        tidyselect_1.1.0   
## [73] xfun_0.20

Multivariate distributions

This section reports a series of multivariate summaries of the NHANES dataset.

Overview

Variable correlation

Correlations of the physical activity variables (outcome)

Variable clustering

Variable clustering is used for assessing collinearity, redundancy, and for separating variables into clusters that can be scored as a single variable, thus resulting in data reduction.

## Hmisc::varclus(x = ~age + gender + bmi + sys + lbxtc + lbdhdd + 
##     smokecigs + drinkstatus + mortstat + diabetes + chf + cancer + 
##     stroke, data = a_nhanes)
## 
## 
## Similarity matrix (Spearman rho^2)
## 
##                             age genderFemale  bmi  sys lbxtc lbdhdd
## age                        1.00         0.00 0.00 0.19  0.00   0.00
## genderFemale               0.00         1.00 0.00 0.00  0.01   0.13
## bmi                        0.00         0.00 1.00 0.02  0.00   0.08
## sys                        0.19         0.00 0.02 1.00  0.00   0.00
## lbxtc                      0.00         0.01 0.00 0.00  1.00   0.02
## lbdhdd                     0.00         0.13 0.08 0.00  0.02   1.00
## smokecigsFormer            0.07         0.02 0.00 0.01  0.00   0.00
## smokecigsCurrent           0.02         0.01 0.01 0.00  0.00   0.01
## drinkstatusNon-Drinker     0.05         0.01 0.01 0.01  0.00   0.01
## drinkstatusHeavy Drinker   0.00         0.01 0.01 0.00  0.00   0.01
## drinkstatusMissing alcohol 0.01         0.00 0.00 0.00  0.00   0.00
## mortstat                   0.17         0.01 0.00 0.04  0.01   0.00
## diabetesYes                0.04         0.00 0.02 0.01  0.01   0.01
## chfYes                     0.03         0.00 0.00 0.00  0.01   0.00
## cancerYes                  0.06         0.00 0.00 0.00  0.00   0.00
## strokeYes                  0.03         0.00 0.00 0.01  0.00   0.00
##                            smokecigsFormer smokecigsCurrent
## age                                   0.07             0.02
## genderFemale                          0.02             0.01
## bmi                                   0.00             0.01
## sys                                   0.01             0.00
## lbxtc                                 0.00             0.00
## lbdhdd                                0.00             0.01
## smokecigsFormer                       1.00             0.12
## smokecigsCurrent                      0.12             1.00
## drinkstatusNon-Drinker                0.00             0.02
## drinkstatusHeavy Drinker              0.00             0.03
## drinkstatusMissing alcohol            0.00             0.00
## mortstat                              0.02             0.00
## diabetesYes                           0.00             0.00
## chfYes                                0.01             0.00
## cancerYes                             0.01             0.00
## strokeYes                             0.00             0.00
##                            drinkstatusNon-Drinker drinkstatusHeavy Drinker
## age                                          0.05                     0.00
## genderFemale                                 0.01                     0.01
## bmi                                          0.01                     0.01
## sys                                          0.01                     0.00
## lbxtc                                        0.00                     0.00
## lbdhdd                                       0.01                     0.01
## smokecigsFormer                              0.00                     0.00
## smokecigsCurrent                             0.02                     0.03
## drinkstatusNon-Drinker                       1.00                     0.04
## drinkstatusHeavy Drinker                     0.04                     1.00
## drinkstatusMissing alcohol                   0.04                     0.01
## mortstat                                     0.02                     0.00
## diabetesYes                                  0.02                     0.00
## chfYes                                       0.01                     0.00
## cancerYes                                    0.00                     0.00
## strokeYes                                    0.01                     0.00
##                            drinkstatusMissing alcohol mortstat diabetesYes
## age                                              0.01     0.17        0.04
## genderFemale                                     0.00     0.01        0.00
## bmi                                              0.00     0.00        0.02
## sys                                              0.00     0.04        0.01
## lbxtc                                            0.00     0.01        0.01
## lbdhdd                                           0.00     0.00        0.01
## smokecigsFormer                                  0.00     0.02        0.00
## smokecigsCurrent                                 0.00     0.00        0.00
## drinkstatusNon-Drinker                           0.04     0.02        0.02
## drinkstatusHeavy Drinker                         0.01     0.00        0.00
## drinkstatusMissing alcohol                       1.00     0.00        0.00
## mortstat                                         0.00     1.00        0.03
## diabetesYes                                      0.00     0.03        1.00
## chfYes                                           0.00     0.04        0.03
## cancerYes                                        0.00     0.03        0.00
## strokeYes                                        0.00     0.03        0.02
##                            chfYes cancerYes strokeYes
## age                          0.03      0.06      0.03
## genderFemale                 0.00      0.00      0.00
## bmi                          0.00      0.00      0.00
## sys                          0.00      0.00      0.01
## lbxtc                        0.01      0.00      0.00
## lbdhdd                       0.00      0.00      0.00
## smokecigsFormer              0.01      0.01      0.00
## smokecigsCurrent             0.00      0.00      0.00
## drinkstatusNon-Drinker       0.01      0.00      0.01
## drinkstatusHeavy Drinker     0.00      0.00      0.00
## drinkstatusMissing alcohol   0.00      0.00      0.00
## mortstat                     0.04      0.03      0.03
## diabetesYes                  0.03      0.00      0.02
## chfYes                       1.00      0.00      0.02
## cancerYes                    0.00      1.00      0.00
## strokeYes                    0.02      0.00      1.00
## 
## No. of observations used for each pair:
## 
##                             age genderFemale  bmi  sys lbxtc lbdhdd
## age                        6680         6680 6624 6360  6410   6410
## genderFemale               6680         6680 6624 6360  6410   6410
## bmi                        6624         6624 6624 6316  6358   6358
## sys                        6360         6360 6316 6360  6133   6133
## lbxtc                      6410         6410 6358 6133  6410   6410
## lbdhdd                     6410         6410 6358 6133  6410   6410
## smokecigsFormer            6676         6676 6621 6356  6406   6406
## smokecigsCurrent           6676         6676 6621 6356  6406   6406
## drinkstatusNon-Drinker     6680         6680 6624 6360  6410   6410
## drinkstatusHeavy Drinker   6680         6680 6624 6360  6410   6410
## drinkstatusMissing alcohol 6680         6680 6624 6360  6410   6410
## mortstat                   6671         6671 6615 6351  6401   6401
## diabetesYes                6680         6680 6624 6360  6410   6410
## chfYes                     6680         6680 6624 6360  6410   6410
## cancerYes                  6680         6680 6624 6360  6410   6410
## strokeYes                  6680         6680 6624 6360  6410   6410
##                            smokecigsFormer smokecigsCurrent
## age                                   6676             6676
## genderFemale                          6676             6676
## bmi                                   6621             6621
## sys                                   6356             6356
## lbxtc                                 6406             6406
## lbdhdd                                6406             6406
## smokecigsFormer                       6676             6676
## smokecigsCurrent                      6676             6676
## drinkstatusNon-Drinker                6676             6676
## drinkstatusHeavy Drinker              6676             6676
## drinkstatusMissing alcohol            6676             6676
## mortstat                              6667             6667
## diabetesYes                           6676             6676
## chfYes                                6676             6676
## cancerYes                             6676             6676
## strokeYes                             6676             6676
##                            drinkstatusNon-Drinker drinkstatusHeavy Drinker
## age                                          6680                     6680
## genderFemale                                 6680                     6680
## bmi                                          6624                     6624
## sys                                          6360                     6360
## lbxtc                                        6410                     6410
## lbdhdd                                       6410                     6410
## smokecigsFormer                              6676                     6676
## smokecigsCurrent                             6676                     6676
## drinkstatusNon-Drinker                       6680                     6680
## drinkstatusHeavy Drinker                     6680                     6680
## drinkstatusMissing alcohol                   6680                     6680
## mortstat                                     6671                     6671
## diabetesYes                                  6680                     6680
## chfYes                                       6680                     6680
## cancerYes                                    6680                     6680
## strokeYes                                    6680                     6680
##                            drinkstatusMissing alcohol mortstat diabetesYes
## age                                              6680     6671        6680
## genderFemale                                     6680     6671        6680
## bmi                                              6624     6615        6624
## sys                                              6360     6351        6360
## lbxtc                                            6410     6401        6410
## lbdhdd                                           6410     6401        6410
## smokecigsFormer                                  6676     6667        6676
## smokecigsCurrent                                 6676     6667        6676
## drinkstatusNon-Drinker                           6680     6671        6680
## drinkstatusHeavy Drinker                         6680     6671        6680
## drinkstatusMissing alcohol                       6680     6671        6680
## mortstat                                         6671     6671        6671
## diabetesYes                                      6680     6671        6680
## chfYes                                           6680     6671        6680
## cancerYes                                        6680     6671        6680
## strokeYes                                        6680     6671        6680
##                            chfYes cancerYes strokeYes
## age                          6680      6680      6680
## genderFemale                 6680      6680      6680
## bmi                          6624      6624      6624
## sys                          6360      6360      6360
## lbxtc                        6410      6410      6410
## lbdhdd                       6410      6410      6410
## smokecigsFormer              6676      6676      6676
## smokecigsCurrent             6676      6676      6676
## drinkstatusNon-Drinker       6680      6680      6680
## drinkstatusHeavy Drinker     6680      6680      6680
## drinkstatusMissing alcohol   6680      6680      6680
## mortstat                     6671      6671      6671
## diabetesYes                  6680      6680      6680
## chfYes                       6680      6680      6680
## cancerYes                    6680      6680      6680
## strokeYes                    6680      6680      6680
## 
## hclust results (method=complete)
## 
## 
## Call:
## hclust(d = as.dist(1 - x), method = method)
## 
## Cluster method   : complete 
## Number of objects: 16

Plot associations.

Variable redundancy

Redundancy analysis of predictor variables.

## 
## Redundancy Analysis
## 
## Hmisc::redun(formula = ~age + gender + bmi + sys + lbxtc + lbdhdd + 
##     smokecigs + drinkstatus + mortstat + diabetes + chf + cancer + 
##     stroke, data = a_nhanes)
## 
## n: 6080  p: 13   nk: 3 
## 
## Number of NAs:    600 
## Frequencies of Missing Values Due to Each Variable
##         age      gender         bmi         sys       lbxtc      lbdhdd 
##           0           0          56         320         270         270 
##   smokecigs drinkstatus    mortstat    diabetes         chf      cancer 
##           4           0           9           0           0           0 
##      stroke 
##           0 
## 
## 
## Transformation of target variables forced to be linear
## 
## R-squared cutoff: 0.9    Type: ordinary 
## 
## R^2 with which each variable can be predicted from all other variables:
## 
##         age      gender         bmi         sys       lbxtc      lbdhdd 
##       0.417       0.222       0.156       0.207       0.057       0.274 
##   smokecigs drinkstatus    mortstat    diabetes         chf      cancer 
##       0.116       0.142       0.282       0.110       0.091       0.080 
##      stroke 
##       0.062 
## 
## No redundant variables

Summary reports by age and gender

Distribution of age by gender

Summary report by age group and gender

Summary report by gender

	N	Male N=3294	Female N=3386
Baseline characteristics by gender.
age years	6680	41.8 53.8 68.0 55.1 ± 15.3	40.8 52.4 66.2 54.0 ± 15.4
body mass index kg/m2	6624	24.99 27.94 31.26 28.58 ± 5.64	24.40 28.31 33.37 29.55 ± 7.10
education level : Less than high school	6673	0.30 ⁹⁷⁴/₃₂₈₉	0.27 ⁹²⁵/₃₃₈₄
High school		0.24 ⁷⁹⁸/₃₂₈₉	0.25 ⁸³⁶/₃₃₈₄
More than high school		0.46 ¹⁵¹⁷/₃₂₈₉	0.48 ¹⁶²³/₃₃₈₄
Systolic blood pressure mg/dl	6360	115.0 125.0 137.0 127.7 ± 18.2	111.0 123.0 139.0 126.8 ± 22.4
Total cholesterol mg/dL	6410	172.0 198.0 225.0 200.6 ± 42.8	178.0 204.0 231.0 207.1 ± 42.6
HDL cholesterol mg/dL	6410	40.0 46.0 56.0 49.0 ± 13.9	48.0 58.0 70.0 60.1 ± 17.2
smoking status : Never	6676	0.38 ¹²⁶⁶/₃₂₉₂	0.59 ¹⁹⁸⁷/₃₃₈₄
Former		0.35 ¹¹⁶⁷/₃₂₉₂	0.23 ⁷⁷⁷/₃₃₈₄
Current		0.26 ⁸⁵⁹/₃₂₉₂	0.18 ⁶²⁰/₃₃₈₄
alcohol consumption : Moderate Drinker	6680	0.56 ¹⁸⁴⁶/₃₂₉₄	0.47 ¹⁶⁰³/₃₃₈₆
Non-Drinker		0.29 ⁹⁶⁴/₃₂₉₄	0.41 ¹³⁷²/₃₃₈₆
Heavy Drinker		0.08 ²⁷⁶/₃₂₉₄	0.05 ¹⁵³/₃₃₈₆
Missing alcohol		0.06 ²⁰⁸/₃₂₉₄	0.08 ²⁵⁸/₃₃₈₆
Final mortality status	6671	0.21 ⁶⁹²/₃₂₉₁	0.14 ⁴⁸⁹/₃₃₈₀
diabetes : Yes	6680	0.13 ⁴²⁵/₃₂₉₄	0.13 ⁴²⁷/₃₃₈₆
congestive heart failure : Yes	6680	0.05 ¹⁶⁰/₃₂₉₄	0.03 ¹⁰⁴/₃₃₈₆
cancer : Yes	6680	0.09 ³⁰⁶/₃₂₉₄	0.11 ³⁶⁶/₃₃₈₆
stroke : Yes	6680	0.04 ¹³⁶/₃₂₉₄	0.04 ¹³⁸/₃₃₈₆
a b c represent the lower quartile a, the median b, and the upper quartile c for continuous variables. x ± s represents X ± 1 SD. N is the number of non-missing values.

Summary report by age group for men

	N	30-44 N=1048	45-59 N=900	60-74 N=931	75+ N=415
Baseline characteristics by gae group for men.
body mass index kg/m2	3272	24.86 27.93 31.32 28.80 ± 6.60	25.35 28.05 31.38 28.78 ± 5.41	25.41 28.23 31.81 28.78 ± 5.10	24.21 26.81 29.72 27.18 ± 4.35
education level : Less than high school	3289	0.25 ²⁵⁹/₁₀₄₈	0.22 ¹⁹⁵/₈₉₈	0.38 ³⁴⁹/₉₃₀	0.41 ¹⁷¹/₄₁₃
High school		0.25 ²⁶⁴/₁₀₄₈	0.26 ²³³/₈₉₈	0.23 ²¹²/₉₃₀	0.22 ⁸⁹/₄₁₃
More than high school		0.50 ⁵²⁵/₁₀₄₈	0.52 ⁴⁷⁰/₈₉₈	0.40 ³⁶⁹/₉₃₀	0.37 ¹⁵³/₄₁₃
Systolic blood pressure mg/dl	3164	112.0 119.0 129.0 121.0 ± 12.4	115.0 123.0 134.5 126.2 ± 17.1	120.0 131.0 145.0 133.3 ± 19.9	120.0 133.0 147.0 134.9 ± 21.9
Total cholesterol mg/dL	3180	177.0 200.0 229.0 204.0 ± 42.1	178.0 204.0 231.0 206.7 ± 42.8	168.0 193.0 222.0 197.0 ± 44.1	158.5 185.0 212.5 187.2 ± 37.6
HDL cholesterol mg/dL	3180	39.0 45.0 54.0 47.8 ± 14.1	40.0 47.0 57.0 49.2 ± 14.1	40.0 46.0 56.0 49.1 ± 13.4	41.0 47.0 58.0 50.7 ± 14.2
smoking status : Never	3292	0.49 ⁵¹⁸/₁₀₄₈	0.39 ³⁵¹/₉₀₀	0.28 ²⁶²/₉₃₀	0.33 ¹³⁵/₄₁₄
Former		0.19 ¹⁹⁶/₁₀₄₈	0.28 ²⁵³/₉₀₀	0.51 ⁴⁷²/₉₃₀	0.59 ²⁴⁶/₄₁₄
Current		0.32 ³³⁴/₁₀₄₈	0.33 ²⁹⁶/₉₀₀	0.21 ¹⁹⁶/₉₃₀	0.08 ³³/₄₁₄
alcohol consumption : Moderate Drinker	3294	0.62 ⁶⁴⁹/₁₀₄₈	0.59 ⁵³³/₉₀₀	0.51 ⁴⁷⁷/₉₃₁	0.45 ¹⁸⁷/₄₁₅
Non-Drinker		0.19 ²⁰¹/₁₀₄₈	0.25 ²²⁶/₉₀₀	0.37 ³⁴⁵/₉₃₁	0.46 ¹⁹²/₄₁₅
Heavy Drinker		0.10 ¹⁰⁴/₁₀₄₈	0.10 ⁸⁷/₉₀₀	0.08 ⁷¹/₉₃₁	0.03 ¹⁴/₄₁₅
Missing alcohol		0.09 ⁹⁴/₁₀₄₈	0.06 ⁵⁴/₉₀₀	0.04 ³⁸/₉₃₁	0.05 ²²/₄₁₅
diabetes : Yes	3294	0.05 ⁴⁹/₁₀₄₈	0.10 ⁹⁰/₉₀₀	0.23 ²¹⁸/₉₃₁	0.16 ⁶⁸/₄₁₅
congestive heart failure : Yes	3294	0.01 ⁶/₁₀₄₈	0.03 ²⁸/₉₀₀	0.09 ⁸⁰/₉₃₁	0.11 ⁴⁶/₄₁₅
cancer : Yes	3294	0.02 ¹⁷/₁₀₄₈	0.04 ³⁹/₉₀₀	0.15 ¹³⁷/₉₃₁	0.27 ¹¹³/₄₁₅
stroke : Yes	3294	0.00 ⁴/₁₀₄₈	0.02 ¹⁵/₉₀₀	0.07 ⁶⁹/₉₃₁	0.12 ⁴⁸/₄₁₅
a b c represent the lower quartile a, the median b, and the upper quartile c for continuous variables. x ± s represents X ± 1 SD. N is the number of non-missing values.

Summary report by age group for women

	N	30-44 N=1164	45-59 N=924	60-74 N=905	75+ N=393
Baseline characteristics by gae group for men.
body mass index kg/m2	3352	23.99 28.00 33.37 29.34 ± 7.26	24.66 29.18 35.06 30.45 ± 7.67	24.92 28.82 33.36 29.86 ± 6.74	23.59 26.82 30.14 27.25 ± 5.31
education level : Less than high school	3384	0.22 ²⁵⁸/₁₁₆₃	0.20 ¹⁸⁶/₉₂₄	0.36 ³²³/₉₀₅	0.40 ¹⁵⁸/₃₉₂
High school		0.20 ²³⁷/₁₁₆₃	0.24 ²²⁶/₉₂₄	0.28 ²⁵⁰/₉₀₅	0.31 ¹²³/₃₉₂
More than high school		0.57 ⁶⁶⁸/₁₁₆₃	0.55 ⁵¹²/₉₂₄	0.37 ³³²/₉₀₅	0.28 ¹¹¹/₃₉₂
Systolic blood pressure mg/dl	3196	104.0 112.0 120.0 113.2 ± 13.4	113.0 123.0 135.0 125.6 ± 19.5	121.0 135.0 150.2 137.2 ± 22.1	131.0 143.0 159.0 145.9 ± 24.9
Total cholesterol mg/dL	3230	170.0 195.0 223.0 199.0 ± 42.5	182.0 208.0 232.0 209.6 ± 41.7	187.0 212.0 239.0 215.0 ± 42.2	176.0 204.0 234.0 207.1 ± 41.8
HDL cholesterol mg/dL	3230	47.0 57.0 69.0 59.5 ± 17.3	47.0 57.0 70.0 60.1 ± 17.5	49.0 57.5 69.0 60.1 ± 16.7	49.0 60.0 73.0 62.0 ± 17.2
smoking status : Never	3384	0.64 ⁷⁴⁵/₁₁₆₄	0.54 ⁴⁹⁹/₉₂₃	0.56 ⁵⁰⁴/₉₀₄	0.61 ²³⁹/₃₉₃
Former		0.14 ¹⁵⁹/₁₁₆₄	0.23 ²¹⁶/₉₂₃	0.30 ²⁷³/₉₀₄	0.33 ¹²⁹/₃₉₃
Current		0.22 ²⁶⁰/₁₁₆₄	0.23 ²⁰⁸/₉₂₃	0.14 ¹²⁷/₉₀₄	0.06 ²⁵/₃₉₃
alcohol consumption : Moderate Drinker	3386	0.57 ⁶⁶¹/₁₁₆₄	0.51 ⁴⁷¹/₉₂₄	0.39 ³⁵²/₉₀₅	0.30 ¹¹⁹/₃₉₃
Non-Drinker		0.29 ³³⁹/₁₁₆₄	0.34 ³¹⁶/₉₂₄	0.53 ⁴⁸⁴/₉₀₅	0.59 ²³³/₃₉₃
Heavy Drinker		0.04 ⁴⁶/₁₁₆₄	0.07 ⁶⁴/₉₂₄	0.03 ³¹/₉₀₅	0.03 ¹²/₃₉₃
Missing alcohol		0.10 ¹¹⁸/₁₁₆₄	0.08 ⁷³/₉₂₄	0.04 ³⁸/₉₀₅	0.07 ²⁹/₃₉₃
diabetes : Yes	3386	0.03 ⁴⁰/₁₁₆₄	0.13 ¹²¹/₉₂₄	0.22 ¹⁹⁵/₉₀₅	0.18 ⁷¹/₃₉₃
congestive heart failure : Yes	3386	0.01 ⁸/₁₁₆₄	0.02 ¹⁹/₉₂₄	0.05 ⁴²/₉₀₅	0.09 ³⁵/₃₉₃
cancer : Yes	3386	0.04 ⁴⁶/₁₁₆₄	0.10 ⁹²/₉₂₄	0.14 ¹³⁰/₉₀₅	0.25 ⁹⁸/₃₉₃
stroke : Yes	3386	0.01 ¹⁵/₁₁₆₄	0.04 ³³/₉₂₄	0.06 ⁵¹/₉₀₅	0.10 ³⁹/₃₉₃
a b c represent the lower quartile a, the median b, and the upper quartile c for continuous variables. x ± s represents X ± 1 SD. N is the number of non-missing values.

Continuous variables by age and gender

Distribution of systolic blood pressure

Distribution of cholesterol

Distribution of BMI

Distribution of wear time

Physical activity data

Distribution of MVPA

Distribution of MVPA and Total log activity count by time of day

Section session info

## R version 4.0.2 (2020-06-22)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 18363)
## 
## Matrix products: default
## 
## locale:
## [1] LC_COLLATE=English_United States.1252 
## [2] LC_CTYPE=English_United States.1252   
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C                          
## [5] LC_TIME=English_United States.1252    
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] gridExtra_2.3   naniar_0.6.0    corrplot_0.84   gtsummary_1.3.6
##  [5] Hmisc_4.5-0     Formula_1.2-4   survival_3.1-12 lattice_0.20-41
##  [9] plotly_4.9.3    forcats_0.5.1   stringr_1.4.0   dplyr_1.0.4    
## [13] purrr_0.3.4     readr_1.4.0     tidyr_1.1.2     tibble_3.0.6   
## [17] ggplot2_3.3.3   tidyverse_1.3.0 here_1.0.1     
## 
## loaded via a namespace (and not attached):
##  [1] nlme_3.1-148        fs_1.5.0            usethis_2.0.1      
##  [4] lubridate_1.7.9.2   RColorBrewer_1.1-2  httr_1.4.2         
##  [7] rprojroot_2.0.2     tools_4.0.2         backports_1.2.1    
## [10] R6_2.5.0            rpart_4.1-15        mgcv_1.8-31        
## [13] DBI_1.1.1           lazyeval_0.2.2      colorspace_2.0-0   
## [16] nnet_7.3-14         withr_2.4.1         tidyselect_1.1.0   
## [19] compiler_4.0.2      cli_2.3.0           rvest_0.3.6        
## [22] gt_0.2.2            htmlTable_2.1.0     xml2_1.3.2         
## [25] labeling_0.4.2      bookdown_0.21       scales_1.1.1       
## [28] checkmate_2.0.0     digest_0.6.27       foreign_0.8-80     
## [31] rmarkdown_2.6       base64enc_0.1-3     jpeg_0.1-8.1       
## [34] pkgconfig_2.0.3     htmltools_0.5.1.1   dbplyr_2.1.0       
## [37] highr_0.8           htmlwidgets_1.5.3   rlang_0.4.10       
## [40] readxl_1.3.1        rstudioapi_0.13     farver_2.0.3       
## [43] generics_0.1.0      jsonlite_1.7.2      crosstalk_1.1.1    
## [46] magrittr_2.0.1      Matrix_1.2-18       Rcpp_1.0.6         
## [49] munsell_0.5.0       lifecycle_0.2.0     visdat_0.5.3       
## [52] stringi_1.5.3       yaml_2.2.1          grid_4.0.2         
## [55] crayon_1.4.1        haven_2.3.1         splines_4.0.2      
## [58] hms_1.0.0           knitr_1.31          pillar_1.4.7       
## [61] reprex_1.0.0        glue_1.4.2          evaluate_0.14      
## [64] latticeExtra_0.6-29 data.table_1.13.6   broom.helpers_1.1.0
## [67] modelr_0.1.8        png_0.1-7           vctrs_0.3.6        
## [70] rmdformats_1.0.1    cellranger_1.1.0    gtable_0.3.0       
## [73] assertthat_0.2.1    xfun_0.20           broom_0.7.4        
## [76] viridisLite_0.3.0   cluster_2.1.0       ellipsis_0.3.1